Solve 3+x^2=103

$$3 + x ^ { 2 } = 103$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Subtract 103 from both sides.

$$3+x^{2}-103=0$$

Subtract 103 from 3 to get -100.

$$-100+x^{2}=0$$

Consider -100+x^{2}. Rewrite -100+x^{2} as x^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)=0$$

To find equation solutions, solve x-10=0 and x+10=0.

$$x=10 x=-10$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$x^{2}=103-3$$

Subtract 3 from 103 to get 100.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

Steps Using the Quadratic Formula

Subtract 103 from both sides.

$$3+x^{2}-103=0$$

Subtract 103 from 3 to get -100.

$$-100+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-100\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-100\right)}}{2}$$

Multiply -4 times -100.

$$x=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$x=\frac{0±20}{2}$$

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

$$x=10$$

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

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$