Solve 289=4x^2

$$289 = 4 x ^ { 2 }$$

Solve for x

$$x = \frac{17}{2} = 8\frac{1}{2} = 8.5$$

$$x = -\frac{17}{2} = -8\frac{1}{2} = -8.5$$

Steps Using Difference of Squares

Divide both sides by 4.

$$\frac{289}{4}=x^{2}$$

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

$$x^{2}=\frac{289}{4}$$

Subtract \frac{289}{4} from both sides.

$$x^{2}-\frac{289}{4}=0$$

Multiply both sides by 4.

$$4x^{2}-289=0$$

Consider 4x^{2}-289. Rewrite 4x^{2}-289 as \left(2x\right)^{2}-17^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(2x-17\right)\left(2x+17\right)=0$$

To find equation solutions, solve 2x-17=0 and 2x+17=0.

$$x=\frac{17}{2} x=-\frac{17}{2}$$

Steps by Finding Square Root

Divide both sides by 4.

$$\frac{289}{4}=x^{2}$$

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

$$x^{2}=\frac{289}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{17}{2} x=-\frac{17}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 4.

$$\frac{289}{4}=x^{2}$$

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

$$x^{2}=\frac{289}{4}$$

Subtract \frac{289}{4} from both sides.

$$x^{2}-\frac{289}{4}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{289}{4} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{289}{4}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{289}{4}\right)}}{2}$$

Multiply -4 times -\frac{289}{4}.

$$x=\frac{0±\sqrt{289}}{2}$$

Take the square root of 289.

$$x=\frac{0±17}{2}$$

Now solve the equation x=\frac{0±17}{2} when ± is plus. Divide 17 by 2.

$$x=\frac{17}{2}$$

Now solve the equation x=\frac{0±17}{2} when ± is minus. Divide -17 by 2.

$$x=-\frac{17}{2}$$

The equation is now solved.

$$x=\frac{17}{2} x=-\frac{17}{2}$$