Solve 1126*76=(76+1126-x)*x

$$1126 \times 76=(76+1126-x) \times x$$

Solve for x

$$x=76$$

$$x=1126$$

Steps Using the Quadratic Formula

Multiply 1126 and 76 to get 85576.

$$85576=\left(76+1126-x\right)x$$

Add 76 and 1126 to get 1202.

$$85576=\left(1202-x\right)x$$

Use the distributive property to multiply 1202-x by x.

$$85576=1202x-x^{2}$$

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

$$1202x-x^{2}=85576$$

Subtract 85576 from both sides.

$$1202x-x^{2}-85576=0$$

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.

$$-x^{2}+1202x-85576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 1202 for b, and -85576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1202±\sqrt{1202^{2}-4\left(-1\right)\left(-85576\right)}}{2\left(-1\right)}$$

Square 1202.

$$x=\frac{-1202±\sqrt{1444804-4\left(-1\right)\left(-85576\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{-1202±\sqrt{1444804+4\left(-85576\right)}}{2\left(-1\right)}$$

Multiply 4 times -85576.

$$x=\frac{-1202±\sqrt{1444804-342304}}{2\left(-1\right)}$$

Add 1444804 to -342304.

$$x=\frac{-1202±\sqrt{1102500}}{2\left(-1\right)}$$

Take the square root of 1102500.

$$x=\frac{-1202±1050}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{-1202±1050}{-2}$$

Now solve the equation x=\frac{-1202±1050}{-2} when ± is plus. Add -1202 to 1050.

$$x=-\frac{152}{-2}$$

Divide -152 by -2.

$$x=76$$

Now solve the equation x=\frac{-1202±1050}{-2} when ± is minus. Subtract 1050 from -1202.

$$x=-\frac{2252}{-2}$$

Divide -2252 by -2.

$$x=1126$$

The equation is now solved.

$$x=76 x=1126$$

Steps for Completing the Square

Multiply 1126 and 76 to get 85576.

$$85576=\left(76+1126-x\right)x$$

Add 76 and 1126 to get 1202.

$$85576=\left(1202-x\right)x$$

Use the distributive property to multiply 1202-x by x.

$$85576=1202x-x^{2}$$

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

$$1202x-x^{2}=85576$$

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.

$$-x^{2}+1202x=85576$$

Divide both sides by -1.

$$\frac{-x^{2}+1202x}{-1}=\frac{85576}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$x^{2}+\frac{1202}{-1}x=\frac{85576}{-1}$$

Divide 1202 by -1.

$$x^{2}-1202x=\frac{85576}{-1}$$

Divide 85576 by -1.

$$x^{2}-1202x=-85576$$

Divide -1202, the coefficient of the x term, by 2 to get -601. Then add the square of -601 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-1202x+\left(-601\right)^{2}=-85576+\left(-601\right)^{2}$$

Square -601.

$$x^{2}-1202x+361201=-85576+361201$$

Add -85576 to 361201.

$$x^{2}-1202x+361201=275625$$

Factor x^{2}-1202x+361201. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-601\right)^{2}=275625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-601\right)^{2}}=\sqrt{275625}$$

Simplify.

$$x-601=525 x-601=-525$$

Add 601 to both sides of the equation.

$$x=1126 x=76$$