Solve sqrt{3x^2-6x+25}=5-x

$$\sqrt { 3 x ^ { 2 } - 6 x + 25 } = 5 - x$$

Solve for x

$$x=-2$$

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(\sqrt{3x^{2}-6x+25}\right)^{2}=\left(5-x\right)^{2}$$

Calculate \sqrt{3x^{2}-6x+25} to the power of 2 and get 3x^{2}-6x+25.

$$3x^{2}-6x+25=\left(5-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5-x\right)^{2}.

$$3x^{2}-6x+25=25-10x+x^{2}$$

Subtract 25 from both sides.

$$3x^{2}-6x+25-25=-10x+x^{2}$$

Subtract 25 from 25 to get 0.

$$3x^{2}-6x=-10x+x^{2}$$

Add 10x to both sides.

$$3x^{2}-6x+10x=x^{2}$$

Combine -6x and 10x to get 4x.

$$3x^{2}+4x=x^{2}$$

Subtract x^{2} from both sides.

$$3x^{2}+4x-x^{2}=0$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

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

Factor out x.

$$x\left(2x+4\right)=0$$

To find equation solutions, solve x=0 and 2x+4=0.

$$x=0 x=-2$$

Substitute 0 for x in the equation \sqrt{3x^{2}-6x+25}=5-x.

$$\sqrt{3\times 0^{2}-6\times 0+25}=5-0$$

Simplify. The value x=0 satisfies the equation.

$$5=5$$

Substitute -2 for x in the equation \sqrt{3x^{2}-6x+25}=5-x.

$$\sqrt{3\left(-2\right)^{2}-6\left(-2\right)+25}=5-\left(-2\right)$$

Simplify. The value x=-2 satisfies the equation.

$$7=7$$

List all solutions of \sqrt{3x^{2}-6x+25}=5-x.

$$x=0 x=-2$$