Question

Use the Quadratic Formula to solve the equation 4x^2−7=4x.

Select one:
a. x=−1/2+√2 or x=−1/2−√2
b. x=7/8+√133/8 or x=7/8-√133/8
c. x=1/2+√2 or x=1/2−√2
d. x=2+4√2 or x=2−4√2

Answer 1

`\large\boxed{x=(1)/(2)-\sqrt2\ or\ x=(1)/(2)+\sqrt2}`

Explanation:

`\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=(-b\pm√(b^2-4ac))/(2a)`

`\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\√(b^2-4ac)=√(128)=√(64\cdot2)=√(64)\cdot\sqrt2=8\sqrt2\\\\x=(-(-4)\pm8\sqrt2)/((2)(4))=(4\pm8\sqrt2)/(8)\qquad\text{simplify by 4}\\\\x=(1\pm2\sqrt2)/(2)\to x=(1)/(2)\pm\sqrt2`