Solve 144=(26-c)c

$$144 = ( 26 - c ) c$$

Solve for c

$$c=8$$

$$c=18$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 26-c by c.

$$144=26c-c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$26c-c^{2}=144$$

Subtract 144 from both sides.

$$26c-c^{2}-144=0$$

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.

$$-c^{2}+26c-144=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 26 for b, and -144 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$c=\frac{-26±\sqrt{26^{2}-4\left(-1\right)\left(-144\right)}}{2\left(-1\right)}$$

Square 26.

$$c=\frac{-26±\sqrt{676-4\left(-1\right)\left(-144\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$c=\frac{-26±\sqrt{676+4\left(-144\right)}}{2\left(-1\right)}$$

Multiply 4 times -144.

$$c=\frac{-26±\sqrt{676-576}}{2\left(-1\right)}$$

Add 676 to -576.

$$c=\frac{-26±\sqrt{100}}{2\left(-1\right)}$$

Take the square root of 100.

$$c=\frac{-26±10}{2\left(-1\right)}$$

Multiply 2 times -1.

$$c=\frac{-26±10}{-2}$$

Now solve the equation c=\frac{-26±10}{-2} when ± is plus. Add -26 to 10.

$$c=-\frac{16}{-2}$$

Divide -16 by -2.

$$c=8$$

Now solve the equation c=\frac{-26±10}{-2} when ± is minus. Subtract 10 from -26.

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

Divide -36 by -2.

$$c=18$$

The equation is now solved.

$$c=8 c=18$$

Steps for Completing the Square

Use the distributive property to multiply 26-c by c.

$$144=26c-c^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$26c-c^{2}=144$$

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.

$$-c^{2}+26c=144$$

Divide both sides by -1.

$$\frac{-c^{2}+26c}{-1}=\frac{144}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$c^{2}+\frac{26}{-1}c=\frac{144}{-1}$$

Divide 26 by -1.

$$c^{2}-26c=\frac{144}{-1}$$

Divide 144 by -1.

$$c^{2}-26c=-144$$

Divide -26, the coefficient of the x term, by 2 to get -13. Then add the square of -13 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$c^{2}-26c+\left(-13\right)^{2}=-144+\left(-13\right)^{2}$$

Square -13.

$$c^{2}-26c+169=-144+169$$

Add -144 to 169.

$$c^{2}-26c+169=25$$

Factor c^{2}-26c+169. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(c-13\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(c-13\right)^{2}}=\sqrt{25}$$

Simplify.

$$c-13=5 c-13=-5$$

Add 13 to both sides of the equation.

$$c=18 c=8$$