Solve x^2+5-2(51)=103

$$x ^ { 2 } + 5 - 2 ( 51 ) = 103$$

Solve for x

$$x=10\sqrt{2}\approx 14.142135624$$

$$x=-10\sqrt{2}\approx -14.142135624$$

Steps by Finding Square Root

Multiply 2 and 51 to get 102.

$$x^{2}+5-102=103$$

Subtract 102 from 5 to get -97.

$$x^{2}-97=103$$

Add 97 to both sides.

$$x^{2}=103+97$$

Add 103 and 97 to get 200.

$$x^{2}=200$$

Take the square root of both sides of the equation.

$$x=10\sqrt{2} x=-10\sqrt{2}$$

Steps Using the Quadratic Formula

Multiply 2 and 51 to get 102.

$$x^{2}+5-102=103$$

Subtract 102 from 5 to get -97.

$$x^{2}-97=103$$

Subtract 103 from both sides.

$$x^{2}-97-103=0$$

Subtract 103 from -97 to get -200.

$$x^{2}-200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-200\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-200\right)}}{2}$$

Multiply -4 times -200.

$$x=\frac{0±\sqrt{800}}{2}$$

Take the square root of 800.

$$x=\frac{0±20\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{2} when ± is plus.

$$x=10\sqrt{2}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{2} when ± is minus.

$$x=-10\sqrt{2}$$

The equation is now solved.

$$x=10\sqrt{2} x=-10\sqrt{2}$$