Solve 3x^2-200=100

$$3 { x }^{ 2 } -200=100$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Subtract 100 from both sides.

$$3x^{2}-200-100=0$$

Subtract 100 from -200 to get -300.

$$3x^{2}-300=0$$

Divide both sides by 3.

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

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

Add 200 to both sides.

$$3x^{2}=100+200$$

Add 100 and 200 to get 300.

$$3x^{2}=300$$

Divide both sides by 3.

$$x^{2}=\frac{300}{3}$$

Divide 300 by 3 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 100 from both sides.

$$3x^{2}-200-100=0$$

Subtract 100 from -200 to get -300.

$$3x^{2}-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-300\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-300\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-300\right)}}{2\times 3}$$

Multiply -12 times -300.

$$x=\frac{0±\sqrt{3600}}{2\times 3}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±60}{6}$$

Now solve the equation x=\frac{0±60}{6} when ± is plus. Divide 60 by 6.

$$x=10$$

Now solve the equation x=\frac{0±60}{6} when ± is minus. Divide -60 by 6.

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$