Question

find the root of quadratic equation 5x^2+2x+7=0 by completing square method​

Answer 1

${ \sf { x } = - \dfrac{1}{5} + \dfrac{ \: \sqrt{ 34 }}{5} \: \: \: \: \: or \: \: \: \: - \dfrac{1}{5} - \dfrac{ \: \sqrt{ 34 }}{5}}$

Step By Step Explanation

• By Completing Square Method

$\implies \sf 5x^2+2x+7=0$

${ \implies \sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$

${ \implies \sf x^2+ \dfrac{2}{5}x = - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: Shifting \: constant \: term \: on \: RHS}$

${ \implies \sf x^2+2 \bigg( \dfrac{2}{10} \bigg) x + {\bigg( \dfrac{2}{10} \bigg)}^{2} = {\bigg( \dfrac{2}{10} \bigg)}^{2} - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Adding \bigg(\dfrac{1}{2} Coefficient \: of \: x\bigg)^2 \: on \: both\: side's }$

${ \implies \sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4}{100} - \dfrac{7}{5} }$

${ \implies \sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4 - 140}{100} }$

${ \implies \sf { \bigg(x + \dfrac{2}{10} \bigg) } = \sqrt{\dfrac{136}{100} } }$

${ \implies \sf { \bigg(x + \dfrac{2}{10} \bigg) } = \sqrt{\dfrac{ {2}^{2} \times 2 \times 17 }{ {10}^{2} } } }$

${ \implies \sf { x + \dfrac{1}{5} } = \dfrac{\pm \: 2\sqrt{ 34 }}{10} }$

${ \implies \sf { x } = \dfrac{\pm \: \sqrt{ 34 }}{5} - \dfrac{1}{5} }$

${ \implies \sf { x } = - \dfrac{1}{5} + \dfrac{ \: \sqrt{ 34 }}{5} \: \: \: \: \: or \: \: \: \: - \dfrac{1}{5} - \dfrac{ \: \sqrt{ 34 }}{5}}$

Answer 2

$\sf 5x^2+2x+</strong>7=0$

$\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout<strong> \: By \: \: 5$

$\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$${\sf x^2+ \dfrac{2}{5}x = - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: Shifting \: constant \: term \: </strong><strong> \: </strong><strong>R</strong></p><p><strong>[tex]\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$${\sf x^2+ \dfrac{2}{5}x = - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: Shifting \: constant \: term \: on \: RHS}$${\sf x^2+2 \bigg( \dfrac{2}{10} \bigg) x + {\bigg( \dfrac{2}{10} \bigg)}^{2} = {\bigg( \dfrac{2}{10} \bigg)}^{2} - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Adding \bigg(\dfrac{1}{2} Coefficient \: of \: x\bigg)^2 \: on \: both\: side's }$

$\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$${\sf x^2+ \dfrac{2}{5}x - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: : \: \: Shifting \: constant \: term \: on \: RHS}$${\sf x^2+2 \bigg( \dfrac{2}{10} \bigg) x + {\bigg( \dfrac{2}{10} \bigg)}^{2} = {\bigg( \dfrac{2}{10} \bigg)}^{2} - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Adding \bigg(\dfrac{1}{2} Coefficient \: of \: x\bigg)^2 \: on \: both\: side's }$${\sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4}{100} - \dfrac{7}{5} }$

$\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$${\sf x^2+ \dfrac{2}{5}x = - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: Shifting \: constant \: term \: on \: RHS}$${\sf x^2+2 \bigg( \dfrac{2}{10} \bigg) x + {\bigg( \dfrac{2}{10} \bigg)}^{2} = {\( \dfrac{2}{10} \bigg)}^{2} - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Adding \bigg(\dfrac{1}{2} Coefficient \: of \: x\bigg)^2 \: on \: both\: side's }$${\sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4}{100} - \dfrac{7}{5} }$${\sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4 - 140}{100} }$

$\sf 5x^2+2x+7=0$${\sf x^2+ \dfrac{2x}{5} + \dfrac{7}{5} =0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Dividing \: Throughout \: By \: \: 5 }$${\sf x^2+ \dfrac{2}{5}x = - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: Shifting \: constant \: term \: on \: RHS}$${\sf x^2+2 \bigg( \dfrac{2}{10} \bigg) x + {\bigg( \dfrac{2}{10} \bigg)}^{2} = {\bigg( \dfrac{2}{10} \bigg)}^{2} - \dfrac{7}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Adding \bigg(\dfrac{1}{2} Coefficient \: of \: x\bigg)^2 \: on \: both\: side's }$${\sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \dfrac{4}{100} - \dfrac{7}{5} }$${\sf { \bigg(x + \dfrac{2}{10} \bigg) }^{2} = \</strong></p><p>}}$