patel is solving 8x² + 16x + 3 = 0. which steps could he use to solve the quadratic equation? select three…

Explanation:

Step1: Start with the quadratic equation

$8x^{2}+16x + 3=0$

Step2: Factor out 8 from the first - two terms

$8(x^{2}+2x)+3 = 0$, then $8(x^{2}+2x)=-3$, so the fifth option is correct.

Step3: Complete the square inside the parentheses

For the expression $x^{2}+2x$, to complete the square we add 1 inside the parentheses. Since we have a factor of 8 outside, we add $8\times1$ to the right - hand side of the equation. $8(x^{2}+2x + 1)=-3 + 8$, so the first option is correct.

Step4: Solve the quadratic equation using the quadratic formula

For a quadratic equation $ax^{2}+bx + c = 0$ ($a = 8$, $b = 16$, $c = 3$), the quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. First, calculate the discriminant $\Delta=b^{2}-4ac=(16)^{2}-4\times8\times3=256 - 96 = 160$. Then $x=\frac{-16\pm\sqrt{160}}{16}=\frac{-16\pm4\sqrt{10}}{16}=-1\pm\frac{\sqrt{10}}{4}=-1\pm\sqrt{\frac{10}{16}}=-1\pm\sqrt{\frac{5}{8}}$. So the second option is correct.

Answer:

1. $8(x^{2}+2x + 1)=-3 + 8$
2. $x=-1\pm\sqrt{\frac{5}{8}}$
3. $8(x^{2}+2x)=-3$