Solve 1035*2=xleft(x-1right)

$$1035 \times 2 = x \left( x-1 \right)$$

Solve for x

$$x=-45$$

$$x=46$$

Steps Using the Quadratic Formula

Multiply 1035 and 2 to get 2070.

$$2070=x\left(x-1\right)$$

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

$$2070=x^{2}-x$$

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

$$x^{2}-x=2070$$

Subtract 2070 from both sides.

$$x^{2}-x-2070=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -1 for b, and -2070 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-2070\right)}}{2}$$

Multiply -4 times -2070.

$$x=\frac{-\left(-1\right)±\sqrt{1+8280}}{2}$$

Add 1 to 8280.

$$x=\frac{-\left(-1\right)±\sqrt{8281}}{2}$$

Take the square root of 8281.

$$x=\frac{-\left(-1\right)±91}{2}$$

The opposite of -1 is 1.

$$x=\frac{1±91}{2}$$

Now solve the equation x=\frac{1±91}{2} when ± is plus. Add 1 to 91.

$$x=\frac{92}{2}$$

Divide 92 by 2.

$$x=46$$

Now solve the equation x=\frac{1±91}{2} when ± is minus. Subtract 91 from 1.

$$x=-\frac{90}{2}$$

Divide -90 by 2.

$$x=-45$$

The equation is now solved.

$$x=46 x=-45$$

Steps for Completing the Square

Multiply 1035 and 2 to get 2070.

$$2070=x\left(x-1\right)$$

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

$$2070=x^{2}-x$$

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

$$x^{2}-x=2070$$

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.

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=2070+\left(-\frac{1}{2}\right)^{2}$$

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

$$x^{2}-x+\frac{1}{4}=2070+\frac{1}{4}$$

Add 2070 to \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=\frac{8281}{4}$$

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}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{8281}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{8281}{4}}$$

Simplify.

$$x-\frac{1}{2}=\frac{91}{2} x-\frac{1}{2}=-\frac{91}{2}$$

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

$$x=46 x=-45$$