Solve 9622.2x+4266000+732000divx*(x-100)=11517681

$$9622.2x+4266000+732000 \div x \times (x-100)=11517681$$

Solve for x

$$x=\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}\approx 688.613984763$$

$$x=-\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}\approx -11.047419944$$

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.

$$9622.2xx+x\times 4266000+732000\left(x-100\right)=11517681x$$

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

$$9622.2x^{2}+x\times 4266000+732000\left(x-100\right)=11517681x$$

Use the distributive property to multiply 732000 by x-100.

$$9622.2x^{2}+x\times 4266000+732000x-73200000=11517681x$$

Combine x\times 4266000 and 732000x to get 4998000x.

$$9622.2x^{2}+4998000x-73200000=11517681x$$

Subtract 11517681x from both sides.

$$9622.2x^{2}+4998000x-73200000-11517681x=0$$

Combine 4998000x and -11517681x to get -6519681x.

$$9622.2x^{2}-6519681x-73200000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9622.2 for a, -6519681 for b, and -73200000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-6519681\right)±\sqrt{\left(-6519681\right)^{2}-4\times 9622.2\left(-73200000\right)}}{2\times 9622.2}$$

Square -6519681.

$$x=\frac{-\left(-6519681\right)±\sqrt{42506240341761-4\times 9622.2\left(-73200000\right)}}{2\times 9622.2}$$

Multiply -4 times 9622.2.

$$x=\frac{-\left(-6519681\right)±\sqrt{42506240341761-38488.8\left(-73200000\right)}}{2\times 9622.2}$$

Multiply -38488.8 times -73200000.

$$x=\frac{-\left(-6519681\right)±\sqrt{42506240341761+2817380160000}}{2\times 9622.2}$$

Add 42506240341761 to 2817380160000.

$$x=\frac{-\left(-6519681\right)±\sqrt{45323620501761}}{2\times 9622.2}$$

Take the square root of 45323620501761.

$$x=\frac{-\left(-6519681\right)±3\sqrt{5035957833529}}{2\times 9622.2}$$

The opposite of -6519681 is 6519681.

$$x=\frac{6519681±3\sqrt{5035957833529}}{2\times 9622.2}$$

Multiply 2 times 9622.2.

$$x=\frac{6519681±3\sqrt{5035957833529}}{19244.4}$$

Now solve the equation x=\frac{6519681±3\sqrt{5035957833529}}{19244.4} when ± is plus. Add 6519681 to 3\sqrt{5035957833529}.

$$x=\frac{3\sqrt{5035957833529}+6519681}{19244.4}$$

Divide 6519681+3\sqrt{5035957833529} by 19244.4 by multiplying 6519681+3\sqrt{5035957833529} by the reciprocal of 19244.4.

$$x=\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}$$

Now solve the equation x=\frac{6519681±3\sqrt{5035957833529}}{19244.4} when ± is minus. Subtract 3\sqrt{5035957833529} from 6519681.

$$x=\frac{6519681-3\sqrt{5035957833529}}{19244.4}$$

Divide 6519681-3\sqrt{5035957833529} by 19244.4 by multiplying 6519681-3\sqrt{5035957833529} by the reciprocal of 19244.4.

$$x=-\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}$$

The equation is now solved.

$$x=\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582} x=-\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}$$

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.

$$9622.2xx+x\times 4266000+732000\left(x-100\right)=11517681x$$

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

$$9622.2x^{2}+x\times 4266000+732000\left(x-100\right)=11517681x$$

Use the distributive property to multiply 732000 by x-100.

$$9622.2x^{2}+x\times 4266000+732000x-73200000=11517681x$$

Combine x\times 4266000 and 732000x to get 4998000x.

$$9622.2x^{2}+4998000x-73200000=11517681x$$

Subtract 11517681x from both sides.

$$9622.2x^{2}+4998000x-73200000-11517681x=0$$

Combine 4998000x and -11517681x to get -6519681x.

$$9622.2x^{2}-6519681x-73200000=0$$

Add 73200000 to both sides. Anything plus zero gives itself.

$$9622.2x^{2}-6519681x=73200000$$

Divide both sides of the equation by 9622.2, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{9622.2x^{2}-6519681x}{9622.2}=\frac{73200000}{9622.2}$$

Dividing by 9622.2 undoes the multiplication by 9622.2.

$$x^{2}+\left(-\frac{6519681}{9622.2}\right)x=\frac{73200000}{9622.2}$$

Divide -6519681 by 9622.2 by multiplying -6519681 by the reciprocal of 9622.2.

$$x^{2}-\frac{1552305}{2291}x=\frac{73200000}{9622.2}$$

Divide 73200000 by 9622.2 by multiplying 73200000 by the reciprocal of 9622.2.

$$x^{2}-\frac{1552305}{2291}x=\frac{122000000}{16037}$$

Divide -\frac{1552305}{2291}, the coefficient of the x term, by 2 to get -\frac{1552305}{4582}. Then add the square of -\frac{1552305}{4582} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{1552305}{2291}x+\left(-\frac{1552305}{4582}\right)^{2}=\frac{122000000}{16037}+\left(-\frac{1552305}{4582}\right)^{2}$$

Square -\frac{1552305}{4582} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{1552305}{2291}x+\frac{2409650813025}{20994724}=\frac{122000000}{16037}+\frac{2409650813025}{20994724}$$

Add \frac{122000000}{16037} to \frac{2409650813025}{20994724} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}-\frac{1552305}{2291}x+\frac{2409650813025}{20994724}=\frac{17985563691175}{146963068}$$

Factor x^{2}-\frac{1552305}{2291}x+\frac{2409650813025}{20994724}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1552305}{4582}\right)^{2}=\frac{17985563691175}{146963068}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1552305}{4582}\right)^{2}}=\sqrt{\frac{17985563691175}{146963068}}$$

Simplify.

$$x-\frac{1552305}{4582}=\frac{5\sqrt{5035957833529}}{32074} x-\frac{1552305}{4582}=-\frac{5\sqrt{5035957833529}}{32074}$$

Add \frac{1552305}{4582} to both sides of the equation.

$$x=\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582} x=-\frac{5\sqrt{5035957833529}}{32074}+\frac{1552305}{4582}$$