Solve 6x^2-17=7

$$6 { x }^{ 2 } -17=7$$

Solve for x

$$x=2$$

$$x=-2$$

Steps Using Difference of Squares

Subtract 7 from both sides.

$$6x^{2}-17-7=0$$

Subtract 7 from -17 to get -24.

$$6x^{2}-24=0$$

Divide both sides by 6.

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

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

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

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

$$x=2 x=-2$$

Steps by Finding Square Root

Add 17 to both sides.

$$6x^{2}=7+17$$

Add 7 and 17 to get 24.

$$6x^{2}=24$$

Divide both sides by 6.

$$x^{2}=\frac{24}{6}$$

Divide 24 by 6 to get 4.

$$x^{2}=4$$

Take the square root of both sides of the equation.

$$x=2 x=-2$$

Steps Using the Quadratic Formula

Subtract 7 from both sides.

$$6x^{2}-17-7=0$$

Subtract 7 from -17 to get -24.

$$6x^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-24\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-24\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-24\right)}}{2\times 6}$$

Multiply -24 times -24.

$$x=\frac{0±\sqrt{576}}{2\times 6}$$

Take the square root of 576.

$$x=\frac{0±24}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±24}{12}$$

Now solve the equation x=\frac{0±24}{12} when ± is plus. Divide 24 by 12.

$$x=2$$

Now solve the equation x=\frac{0±24}{12} when ± is minus. Divide -24 by 12.

$$x=-2$$

The equation is now solved.

$$x=2 x=-2$$