Solve 34-x=288/x

$$34 - x = \frac { 288 } { x }$$

Solve for x

$$x=16$$

$$x=18$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 34-xx=288$$

Multiply x and x to get x^{2}.

$$x\times 34-x^{2}=288$$

Subtract 288 from both sides.

$$x\times 34-x^{2}-288=0$$

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.

$$-x^{2}+34x-288=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 34 for b, and -288 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-34±\sqrt{34^{2}-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

Square 34.

$$x=\frac{-34±\sqrt{1156-4\left(-1\right)\left(-288\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-34±\sqrt{1156+4\left(-288\right)}}{2\left(-1\right)}$$

Multiply 4 times -288.

$$x=\frac{-34±\sqrt{1156-1152}}{2\left(-1\right)}$$

Add 1156 to -1152.

$$x=\frac{-34±\sqrt{4}}{2\left(-1\right)}$$

Take the square root of 4.

$$x=\frac{-34±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-34±2}{-2}$$

Now solve the equation x=\frac{-34±2}{-2} when ± is plus. Add -34 to 2.

$$x=-\frac{32}{-2}$$

Divide -32 by -2.

$$x=16$$

Now solve the equation x=\frac{-34±2}{-2} when ± is minus. Subtract 2 from -34.

$$x=-\frac{36}{-2}$$

Divide -36 by -2.

$$x=18$$

The equation is now solved.

$$x=16 x=18$$

Steps for Completing the Square

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by x.

$$x\times 34-xx=288$$

Multiply x and x to get x^{2}.

$$x\times 34-x^{2}=288$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$-x^{2}+34x=288$$

Divide both sides by -1.

$$\frac{-x^{2}+34x}{-1}=\frac{288}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{34}{-1}x=\frac{288}{-1}$$

Divide 34 by -1.

$$x^{2}-34x=\frac{288}{-1}$$

Divide 288 by -1.

$$x^{2}-34x=-288$$

Divide -34, the coefficient of the x term, by 2 to get -17. Then add the square of -17 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-34x+\left(-17\right)^{2}=-288+\left(-17\right)^{2}$$

Square -17.

$$x^{2}-34x+289=-288+289$$

Add -288 to 289.

$$x^{2}-34x+289=1$$

Factor x^{2}-34x+289. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-17\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-17\right)^{2}}=\sqrt{1}$$

Simplify.

$$x-17=1 x-17=-1$$

Add 17 to both sides of the equation.

$$x=18 x=16$$