Question

use the quadratic formula to solve for x.
4x² = 4x + 1
round your answer to the nearest hundredth.
if there is more than one solution, separate them with commas.
x =

Explanation:

Step1: Rewrite in standard form

Rewrite $4x^{2}=4x + 1$ as $4x^{2}-4x - 1=0$. Here $a = 4$, $b=-4$, $c=-1$.

Step2: Apply quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute $a = 4$, $b=-4$, $c=-1$ into it: $x=\frac{-(-4)\pm\sqrt{(-4)^{2}-4\times4\times(-1)}}{2\times4}=\frac{4\pm\sqrt{16 + 16}}{8}=\frac{4\pm\sqrt{32}}{8}=\frac{4\pm4\sqrt{2}}{8}=\frac{1\pm\sqrt{2}}{2}$.

Step3: Calculate values and round

For $x=\frac{1+\sqrt{2}}{2}$, $x=\frac{1 + 1.414}{2}=\frac{2.414}{2}=1.21$. For $x=\frac{1-\sqrt{2}}{2}$, $x=\frac{1-1.414}{2}=\frac{-0.414}{2}=-0.21$.

Answer:

$x = 1.21,-0.21$