Solve 6x^2+3(x^2+3)=90

$$6 { x }^{ 2 } +3( { x }^{ 2 } +3) = 90$$

Solve for x

$$x=3$$

$$x=-3$$

Steps Using Difference of Squares

Use the distributive property to multiply 3 by x^{2}+3.

$$6x^{2}+3x^{2}+9=90$$

Combine 6x^{2} and 3x^{2} to get 9x^{2}.

$$9x^{2}+9=90$$

Subtract 90 from both sides.

$$9x^{2}+9-90=0$$

Subtract 90 from 9 to get -81.

$$9x^{2}-81=0$$

Divide both sides by 9.

$$x^{2}-9=0$$

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

To find equation solutions, solve x-3=0 and x+3=0.

$$x=3 x=-3$$

Steps by Finding Square Root

Use the distributive property to multiply 3 by x^{2}+3.

$$6x^{2}+3x^{2}+9=90$$

Combine 6x^{2} and 3x^{2} to get 9x^{2}.

$$9x^{2}+9=90$$

Subtract 9 from both sides.

$$9x^{2}=90-9$$

Subtract 9 from 90 to get 81.

$$9x^{2}=81$$

Divide both sides by 9.

$$x^{2}=\frac{81}{9}$$

Divide 81 by 9 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3 by x^{2}+3.

$$6x^{2}+3x^{2}+9=90$$

Combine 6x^{2} and 3x^{2} to get 9x^{2}.

$$9x^{2}+9=90$$

Subtract 90 from both sides.

$$9x^{2}+9-90=0$$

Subtract 90 from 9 to get -81.

$$9x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 9\left(-81\right)}}{2\times 9}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 9\left(-81\right)}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{0±\sqrt{-36\left(-81\right)}}{2\times 9}$$

Multiply -36 times -81.

$$x=\frac{0±\sqrt{2916}}{2\times 9}$$

Take the square root of 2916.

$$x=\frac{0±54}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{0±54}{18}$$

Now solve the equation x=\frac{0±54}{18} when ± is plus. Divide 54 by 18.

$$x=3$$

Now solve the equation x=\frac{0±54}{18} when ± is minus. Divide -54 by 18.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$