Solve 4x+3sqrt{1-x^2}=0

$$4 x + 3 \sqrt { 1 - x ^ { 2 } } = 0$$

Solve for x

$$x=-\frac{3}{5}=-0.6$$

Solution Steps

Subtract 4x from both sides of the equation.

$$3\sqrt{1-x^{2}}=-4x$$

Square both sides of the equation.

$$\left(3\sqrt{1-x^{2}}\right)^{2}=\left(-4x\right)^{2}$$

Expand \left(3\sqrt{1-x^{2}}\right)^{2}.

$$3^{2}\left(\sqrt{1-x^{2}}\right)^{2}=\left(-4x\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{1-x^{2}}\right)^{2}=\left(-4x\right)^{2}$$

Calculate \sqrt{1-x^{2}} to the power of 2 and get 1-x^{2}.

$$9\left(1-x^{2}\right)=\left(-4x\right)^{2}$$

Use the distributive property to multiply 9 by 1-x^{2}.

$$9-9x^{2}=\left(-4x\right)^{2}$$

Expand \left(-4x\right)^{2}.

$$9-9x^{2}=\left(-4\right)^{2}x^{2}$$

Calculate -4 to the power of 2 and get 16.

$$9-9x^{2}=16x^{2}$$

Subtract 16x^{2} from both sides.

$$9-9x^{2}-16x^{2}=0$$

Combine -9x^{2} and -16x^{2} to get -25x^{2}.

$$9-25x^{2}=0$$

Subtract 9 from both sides. Anything subtracted from zero gives its negation.

$$-25x^{2}=-9$$

Divide both sides by -25.

$$x^{2}=\frac{-9}{-25}$$

Fraction \frac{-9}{-25} can be simplified to \frac{9}{25} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{9}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{3}{5} x=-\frac{3}{5}$$

Substitute \frac{3}{5} for x in the equation 4x+3\sqrt{1-x^{2}}=0.

$$4\times \frac{3}{5}+3\sqrt{1-\left(\frac{3}{5}\right)^{2}}=0$$

Simplify. The value x=\frac{3}{5} does not satisfy the equation.

$$\frac{24}{5}=0$$

Substitute -\frac{3}{5} for x in the equation 4x+3\sqrt{1-x^{2}}=0.

$$4\left(-\frac{3}{5}\right)+3\sqrt{1-\left(-\frac{3}{5}\right)^{2}}=0$$

Simplify. The value x=-\frac{3}{5} satisfies the equation.

$$0=0$$

Equation 3\sqrt{1-x^{2}}=-4x has a unique solution.

$$x=-\frac{3}{5}$$