Question

Solve by completing the square. 4x^2 + 8x– 3=0

Answer 1

Answer:

x = -1 + $\sqrt{\frac{7}{4} }$, x = -1 - $\sqrt{\frac{7}{4} }$

Step-by-step explanation:

4$x^{2}$ + 8x - 3 = 0

First, add 3 to both sides:

4$x^{2}$ + 8x = 3

Next, divide both sides by 4:

$x^{2}$ + 2x = $\frac{3}{4}$

Now, add the correct number by dividing 2 by 2 and squaring it and add it to both sides:

$x^{2}$ + 2x + 1 = $\frac{7}{4}$

Then, factor the left side:

$(x + 1)^{2}$ = $\frac{7}{4}$

Next, take the square root of both sides:

x + 1 = ± $\sqrt{\frac{7}{4} }$

Solve for x:

x = -1 + $\sqrt{\frac{7}{4} }$, x = -1 - $\sqrt{\frac{7}{4} }$