Solve (2x^2-5)=3(2-3x^2)

$$( 2 x ^ { 2 } - 5 ) = 3 ( 2 - 3 x ^ { 2 } )$$

Solve for x

$$x=1$$

$$x=-1$$

Steps Using Difference of Squares

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

$$2x^{2}-5=6-9x^{2}$$

Subtract 6 from both sides.

$$2x^{2}-5-6=-9x^{2}$$

Subtract 6 from -5 to get -11.

$$2x^{2}-11=-9x^{2}$$

Add 9x^{2} to both sides.

$$2x^{2}-11+9x^{2}=0$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}-11=0$$

Divide both sides by 11.

$$x^{2}-1=0$$

Consider x^{2}-1. Rewrite x^{2}-1 as x^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-1\right)\left(x+1\right)=0$$

To find equation solutions, solve x-1=0 and x+1=0.

$$x=1 x=-1$$

Steps by Finding Square Root

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

$$2x^{2}-5=6-9x^{2}$$

Add 9x^{2} to both sides.

$$2x^{2}-5+9x^{2}=6$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}-5=6$$

Add 5 to both sides.

$$11x^{2}=6+5$$

Add 6 and 5 to get 11.

$$11x^{2}=11$$

Divide both sides by 11.

$$x^{2}=\frac{11}{11}$$

Divide 11 by 11 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

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

$$2x^{2}-5=6-9x^{2}$$

Subtract 6 from both sides.

$$2x^{2}-5-6=-9x^{2}$$

Subtract 6 from -5 to get -11.

$$2x^{2}-11=-9x^{2}$$

Add 9x^{2} to both sides.

$$2x^{2}-11+9x^{2}=0$$

Combine 2x^{2} and 9x^{2} to get 11x^{2}.

$$11x^{2}-11=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -11 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-11\right)}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-11\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\left(-11\right)}}{2\times 11}$$

Multiply -44 times -11.

$$x=\frac{0±\sqrt{484}}{2\times 11}$$

Take the square root of 484.

$$x=\frac{0±22}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±22}{22}$$

Now solve the equation x=\frac{0±22}{22} when ± is plus. Divide 22 by 22.

$$x=1$$

Now solve the equation x=\frac{0±22}{22} when ± is minus. Divide -22 by 22.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$