Question

Solve by completing the square :

4x^2-12x+7=0

Answer 1

Answer:

$x=\frac{3}{2}\pm\frac{\sqrt{2}}{2}}$

Step-by-step explanation:

we have

$4x^2-12x+7=0$

step 1

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$4x^2-12x=-7$

step 2

factor the leading coefficient

$4(x^2-3x)=-7$

step 3

Complete the square. Remember to balance the equation by adding the same constants to each side

$4(x^2-3x+1.5^2)=-7+1.5^2(4)$

$4(x^2-3x+2.25)=2$

simplify

$(x^2-3x+2.25)=0.5$

step 4

Rewrite as perfect squares

$(x-1.5)^2=0.5$

step 5

take square root both sides

$x-1.5=\pm\frac{1}{\sqrt{2}}$

Convert 1.5 in a fraction number

$x-\frac{3}{2}=\pm\frac{1}{\sqrt{2}}$

$x=\frac{3}{2}\pm\frac{\sqrt{2}}{2}}$