Question

(x−5)^2+3x-2=0
Quadratic equation​

Answer 1

ANSWER:

$x = \frac{ - 7 + \sqrt{ - 43} }{2}$

EXPLANATION:

$(x - 5)^{2} + 3x - 2 = 0$

$( \: (x)^{2} - 2(x)(5) + {(5)}^{2} \: ) + 3x - 2 = 0$

${x}^{2} - 10x + 25 + 3x - 2 = 0$

${x}^{2} - 10x + 3x + 25 - 2 = 0$

${x}^{2} - 7x + 23 = 0$

${x}^{2} - 7x = - 23$

$adding \: \frac{49}{4} \: on \: both \: sides$

${x}^{2} - 7x + \frac{49}{4} = - 23 + \frac{49}{4}$

$(x)^{2} - 2(x)( \frac{7}{2}) + (\frac{7}{2})^{2} = \frac{ - 92}{4} + \frac{49}{4}$

${(x + \frac{7}{2}) }^{2} = \frac{ - 92 + 49}{4}$

${(x + \frac{7}{2}) }^{2} = \frac{ - 43}{4}$

$taking \: swuare \: root \: on \: both \: sides$

$\sqrt{ {(x + \frac{7}{2} )}^{2} } = \sqrt{ \frac{ - 43}{4} }$

$x + \frac{7}{2} = \frac{ \sqrt{ - 43} }{2}$

$x = - \frac{7}{2} + \frac{ \sqrt{ - 43} }{2}$

$x = \frac{ - 7 + \sqrt{ - 43} }{2}$

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