Solve x-15sqrt{x}+56=0

$$x - 15 \sqrt { x } + 56 = 0$$

Solve for x

$$x=64$$

$$x=49$$

Solution Steps

Subtract 56 from both sides. Anything subtracted from zero gives its negation.

$$x-15\sqrt{x}=-56$$

Subtract x from both sides of the equation.

$$-15\sqrt{x}=-56-x$$

Square both sides of the equation.

$$\left(-15\sqrt{x}\right)^{2}=\left(-56-x\right)^{2}$$

Expand \left(-15\sqrt{x}\right)^{2}.

$$\left(-15\right)^{2}\left(\sqrt{x}\right)^{2}=\left(-56-x\right)^{2}$$

Calculate -15 to the power of 2 and get 225.

$$225\left(\sqrt{x}\right)^{2}=\left(-56-x\right)^{2}$$

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

$$225x=\left(-56-x\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-56-x\right)^{2}.

$$225x=3136+112x+x^{2}$$

Subtract 112x from both sides.

$$225x-112x=3136+x^{2}$$

Combine 225x and -112x to get 113x.

$$113x=3136+x^{2}$$

Subtract x^{2} from both sides.

$$113x-x^{2}=3136$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-x^{2}+113x=3136$$

Subtract 3136 from both sides of the equation.

$$-x^{2}+113x-3136=3136-3136$$

Subtracting 3136 from itself leaves 0.

$$-x^{2}+113x-3136=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 113 for b, and -3136 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-113±\sqrt{113^{2}-4\left(-1\right)\left(-3136\right)}}{2\left(-1\right)}$$

Square 113.

$$x=\frac{-113±\sqrt{12769-4\left(-1\right)\left(-3136\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-113±\sqrt{12769+4\left(-3136\right)}}{2\left(-1\right)}$$

Multiply 4 times -3136.

$$x=\frac{-113±\sqrt{12769-12544}}{2\left(-1\right)}$$

Add 12769 to -12544.

$$x=\frac{-113±\sqrt{225}}{2\left(-1\right)}$$

Take the square root of 225.

$$x=\frac{-113±15}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-113±15}{-2}$$

Now solve the equation x=\frac{-113±15}{-2} when ± is plus. Add -113 to 15.

$$x=-\frac{98}{-2}$$

Divide -98 by -2.

$$x=49$$

Now solve the equation x=\frac{-113±15}{-2} when ± is minus. Subtract 15 from -113.

$$x=-\frac{128}{-2}$$

Divide -128 by -2.

$$x=64$$

The equation is now solved.

$$x=49 x=64$$

Substitute 49 for x in the equation x-15\sqrt{x}+56=0.

$$49-15\sqrt{49}+56=0$$

Simplify. The value x=49 satisfies the equation.

$$0=0$$

Substitute 64 for x in the equation x-15\sqrt{x}+56=0.

$$64-15\sqrt{64}+56=0$$

Simplify. The value x=64 satisfies the equation.

$$0=0$$

List all solutions of -15\sqrt{x}=-x-56.

$$x=49 x=64$$