Algebra

Question

Solve for x -

10x² - 29x + 10 = 0

Provide the steps.

Answer 1

For the polynomial of the form $a.x^2 + b.x +c$, rewrite the middle term as $sum$ of two numbers whose product = $a*c = 10*10=100$ and sum is $b = -29$

$10.x^2 - 25.x - 4.x + 10 = 0$                                         $\because \begin{Bmatrix} -29 = -25 + (- 4) & \\ 100 = -25 * (-4)& \end{Bmatrix}$

 

$5.x(2x - 5) -2(2x - 5) = 0$

 

$(2x - 5).(5x - 2) = 0 $

 

$2x- 5 = 0$

 

$x = 5/2$

    $or$

 

$5x - 2 = 0$

 

$x = 2 / 5$