Solve 2x^2+7=207

$$2 x ^ { 2 } + 7 = 207$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Subtract 207 from both sides.

$$2x^{2}+7-207=0$$

Subtract 207 from 7 to get -200.

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

Divide both sides by 2.

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

Consider x^{2}-100. Rewrite x^{2}-100 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 7 from both sides.

$$2x^{2}=207-7$$

Subtract 7 from 207 to get 200.

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

Divide both sides by 2.

$$x^{2}=\frac{200}{2}$$

Divide 200 by 2 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 207 from both sides.

$$2x^{2}+7-207=0$$

Subtract 207 from 7 to get -200.

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

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

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

Square 0.

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

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-200\right)}}{2\times 2}$$

Multiply -8 times -200.

$$x=\frac{0±\sqrt{1600}}{2\times 2}$$

Take the square root of 1600.

$$x=\frac{0±40}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±40}{4}$$

Now solve the equation x=\frac{0±40}{4} when ± is plus. Divide 40 by 4.

$$x=10$$

Now solve the equation x=\frac{0±40}{4} when ± is minus. Divide -40 by 4.

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$