Question

find the roots of a quadratic equation 5x²+7x-6=0 by completing square method

Answer 1

5x square + 7x - 6 = 5x square + 10x - 3x - 6
= 5x(x + 2) - 3(x + 2) = (5x - 3) (x + 2).
Hence, your answer is x = 3/5 (or) x = -2.

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Answer 2

Answer:

The roots are $x=\frac{3}{5},-2$

Step-by-step explanation:

Given : Equation $5x^2+7x-6=0$

To find : The roots of a quadratic equation by completing square method ?

Solution :

Equation $5x^2+7x-6=0$

Divide both side by 5,

$x^2+\frac{7}{5}x-\frac{6}{5}=0$

Applying completing the square,

$x^2+\frac{7}{5}x-\frac{6}{5}+(\frac{7}{10})^2-(\frac{7}{10})^2=0$

$(x+\frac{7}{10})^2-\frac{6}{5}-\frac{49}{100}=0$

$(x+\frac{7}{10})^2-\frac{169}{100}=0$

$(x+\frac{7}{10})^2=\frac{169}{100}$

Taking root both side,

$x+\frac{7}{10}=\pm\frac{13}{10}$

Take positive,

$x=\frac{13}{10}-\frac{7}{10}$

$x=\frac{6}{10}$

$x=\frac{3}{5}$

Take negative,

$x=-\frac{13}{10}-\frac{7}{10}$

$x=\frac{-20}{10}$

$x=-2$

Therefore, the roots are $x=\frac{3}{5},-2$