Solve sqrt{4x^2-15}-2x=-1

$$\sqrt { 4 x ^ { 2 } - 15 } - 2 x = - 1$$

Solve for x

$$x=4$$

Solution Steps

Subtract -2x from both sides of the equation.

$$\sqrt{4x^{2}-15}=-1+2x$$

Square both sides of the equation.

$$\left(\sqrt{4x^{2}-15}\right)^{2}=\left(-1+2x\right)^{2}$$

Calculate \sqrt{4x^{2}-15} to the power of 2 and get 4x^{2}-15.

$$4x^{2}-15=\left(-1+2x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(-1+2x\right)^{2}.

$$4x^{2}-15=1-4x+4x^{2}$$

Add 4x to both sides.

$$4x^{2}-15+4x=1+4x^{2}$$

Subtract 4x^{2} from both sides.

$$4x^{2}-15+4x-4x^{2}=1$$

Combine 4x^{2} and -4x^{2} to get 0.

$$-15+4x=1$$

Add 15 to both sides.

$$4x=1+15$$

Add 1 and 15 to get 16.

$$4x=16$$

Divide both sides by 4.

$$x=\frac{16}{4}$$

Divide 16 by 4 to get 4.

$$x=4$$

Substitute 4 for x in the equation \sqrt{4x^{2}-15}-2x=-1.

$$\sqrt{4\times 4^{2}-15}-2\times 4=-1$$

Simplify. The value x=4 satisfies the equation.

$$-1=-1$$

Equation \sqrt{4x^{2}-15}=2x-1 has a unique solution.

$$x=4$$