Question

Solve the equation for all values of x by completing the square. 5x^2-70x=-230

Answer 1

$\sf x=\pm \sqrt{3}+7$

solving step wise:

$\sf 5x^2-70x=-230$

divide the following by 5

$\sf x^2-14x=-46$

completing square

$\sf (x-\dfrac{14}{2})^2-(\dfrac{14}{2})^2 =-46$

should look like this

$\sf (x-7)^2-49=-46$

simplify by changing sides

$\sf x-7=\pm \sqrt{3}$

final answer:

$\sf x=\pm \sqrt{3}+7$

Answer 2

Answer:

$x=7 + \sqrt{3}$

$x=7 - \sqrt{3}$

Step-by-step explanation:

Given equation:

$5x^2-70x=-230$

Divide both sides by 5:

$x^2-14x=-46$

Square half of the coefficient of $x$:  $(-14 \div 2)^2=49$
and add this to both sides:

$x^2-14x+49=-46+49$

Factor the left side and simplify the right side:

$(x-7)^2=3$

Square root both sides:

$x-7=\pm\sqrt{3}$

Add 7 to both sides:

$x=7 \pm \sqrt{3}$