Solve 4x^2-100=4left(x-3right)^2

$$4 { x }^{ 2 } -100=4 { \left(x-3 \right) }^{ 2 }$$

Solve for x

$$x = \frac{17}{3} = 5\frac{2}{3} \approx 5.666666667$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$4x^{2}-100=4\left(x^{2}-6x+9\right)$$

Use the distributive property to multiply 4 by x^{2}-6x+9.

$$4x^{2}-100=4x^{2}-24x+36$$

Subtract 4x^{2} from both sides.

$$4x^{2}-100-4x^{2}=-24x+36$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-100=-24x+36$$

Swap sides so that all variable terms are on the left hand side.

$$-24x+36=-100$$

Subtract 36 from both sides.

$$-24x=-100-36$$

Subtract 36 from -100 to get -136.

$$-24x=-136$$

Divide both sides by -24.

$$x=\frac{-136}{-24}$$

Reduce the fraction \frac{-136}{-24} to lowest terms by extracting and canceling out -8.

$$x=\frac{17}{3}$$