Solve x(x-1)div2=10

$$x(x-1) \div 2=10$$

Solve for x

$$x=5$$

$$x=-4$$

Steps Using the Quadratic Formula

Multiply both sides by 2.

$$x\left(x-1\right)=10\times 2$$

Use the distributive property to multiply x by x-1.

$$x^{2}-x=10\times 2$$

Multiply 10 and 2 to get 20.

$$x^{2}-x=20$$

Subtract 20 from both sides.

$$x^{2}-x-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -1 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-20\right)}}{2}$$

Multiply -4 times -20.

$$x=\frac{-\left(-1\right)±\sqrt{1+80}}{2}$$

Add 1 to 80.

$$x=\frac{-\left(-1\right)±\sqrt{81}}{2}$$

Take the square root of 81.

$$x=\frac{-\left(-1\right)±9}{2}$$

The opposite of -1 is 1.

$$x=\frac{1±9}{2}$$

Now solve the equation x=\frac{1±9}{2} when ± is plus. Add 1 to 9.

$$x=\frac{10}{2}$$

Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{1±9}{2} when ± is minus. Subtract 9 from 1.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=5 x=-4$$

Steps for Completing the Square

Multiply both sides by 2.

$$x\left(x-1\right)=10\times 2$$

Use the distributive property to multiply x by x-1.

$$x^{2}-x=10\times 2$$

Multiply 10 and 2 to get 20.

$$x^{2}-x=20$$

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=20+\left(-\frac{1}{2}\right)^{2}$$

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-x+\frac{1}{4}=20+\frac{1}{4}$$

Add 20 to \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=\frac{81}{4}$$

Factor x^{2}-x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Simplify.

$$x-\frac{1}{2}=\frac{9}{2} x-\frac{1}{2}=-\frac{9}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$x=5 x=-4$$