Solve 700+7x=57*56-57*160/250xx

$$700+7x = 57 \cdot 56- \frac{ 57 \cdot 160 }{ 250 } xx$$

Solve for x

$$x = \frac{5 \sqrt{9092041} - 175}{1824} \approx 8.169685159$$

$$x=\frac{-5\sqrt{9092041}-175}{1824}\approx -8.361571123$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 250.

$$175000+1750x=14250\times 56-57\times 160xx$$

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

$$175000+1750x=14250\times 56-57\times 160x^{2}$$

Multiply 14250 and 56 to get 798000.

$$175000+1750x=798000-57\times 160x^{2}$$

Multiply 57 and 160 to get 9120.

$$175000+1750x=798000-9120x^{2}$$

Subtract 798000 from both sides.

$$175000+1750x-798000=-9120x^{2}$$

Subtract 798000 from 175000 to get -623000.

$$-623000+1750x=-9120x^{2}$$

Add 9120x^{2} to both sides.

$$-623000+1750x+9120x^{2}=0$$

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.

$$9120x^{2}+1750x-623000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9120 for a, 1750 for b, and -623000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-1750±\sqrt{1750^{2}-4\times 9120\left(-623000\right)}}{2\times 9120}$$

Square 1750.

$$x=\frac{-1750±\sqrt{3062500-4\times 9120\left(-623000\right)}}{2\times 9120}$$

Multiply -4 times 9120.

$$x=\frac{-1750±\sqrt{3062500-36480\left(-623000\right)}}{2\times 9120}$$

Multiply -36480 times -623000.

$$x=\frac{-1750±\sqrt{3062500+22727040000}}{2\times 9120}$$

Add 3062500 to 22727040000.

$$x=\frac{-1750±\sqrt{22730102500}}{2\times 9120}$$

Take the square root of 22730102500.

$$x=\frac{-1750±50\sqrt{9092041}}{2\times 9120}$$

Multiply 2 times 9120.

$$x=\frac{-1750±50\sqrt{9092041}}{18240}$$

Now solve the equation x=\frac{-1750±50\sqrt{9092041}}{18240} when ± is plus. Add -1750 to 50\sqrt{9092041}.

$$x=\frac{50\sqrt{9092041}-1750}{18240}$$

Divide -1750+50\sqrt{9092041} by 18240.

$$x=\frac{5\sqrt{9092041}-175}{1824}$$

Now solve the equation x=\frac{-1750±50\sqrt{9092041}}{18240} when ± is minus. Subtract 50\sqrt{9092041} from -1750.

$$x=\frac{-50\sqrt{9092041}-1750}{18240}$$

Divide -1750-50\sqrt{9092041} by 18240.

$$x=\frac{-5\sqrt{9092041}-175}{1824}$$

The equation is now solved.

$$x=\frac{5\sqrt{9092041}-175}{1824} x=\frac{-5\sqrt{9092041}-175}{1824}$$

Steps for Completing the Square

Multiply both sides of the equation by 250.

$$175000+1750x=14250\times 56-57\times 160xx$$

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

$$175000+1750x=14250\times 56-57\times 160x^{2}$$

Multiply 14250 and 56 to get 798000.

$$175000+1750x=798000-57\times 160x^{2}$$

Multiply 57 and 160 to get 9120.

$$175000+1750x=798000-9120x^{2}$$

Add 9120x^{2} to both sides.

$$175000+1750x+9120x^{2}=798000$$

Subtract 175000 from both sides.

$$1750x+9120x^{2}=798000-175000$$

Subtract 175000 from 798000 to get 623000.

$$1750x+9120x^{2}=623000$$

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.

$$9120x^{2}+1750x=623000$$

Divide both sides by 9120.

$$\frac{9120x^{2}+1750x}{9120}=\frac{623000}{9120}$$

Dividing by 9120 undoes the multiplication by 9120.

$$x^{2}+\frac{1750}{9120}x=\frac{623000}{9120}$$

Reduce the fraction \frac{1750}{9120} to lowest terms by extracting and canceling out 10.

$$x^{2}+\frac{175}{912}x=\frac{623000}{9120}$$

Reduce the fraction \frac{623000}{9120} to lowest terms by extracting and canceling out 40.

$$x^{2}+\frac{175}{912}x=\frac{15575}{228}$$

Divide \frac{175}{912}, the coefficient of the x term, by 2 to get \frac{175}{1824}. Then add the square of \frac{175}{1824} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{175}{912}x+\left(\frac{175}{1824}\right)^{2}=\frac{15575}{228}+\left(\frac{175}{1824}\right)^{2}$$

Square \frac{175}{1824} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{175}{912}x+\frac{30625}{3326976}=\frac{15575}{228}+\frac{30625}{3326976}$$

Add \frac{15575}{228} to \frac{30625}{3326976} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{175}{912}x+\frac{30625}{3326976}=\frac{227301025}{3326976}$$

Factor x^{2}+\frac{175}{912}x+\frac{30625}{3326976}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{175}{1824}\right)^{2}=\frac{227301025}{3326976}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{175}{1824}\right)^{2}}=\sqrt{\frac{227301025}{3326976}}$$

Simplify.

$$x+\frac{175}{1824}=\frac{5\sqrt{9092041}}{1824} x+\frac{175}{1824}=-\frac{5\sqrt{9092041}}{1824}$$

Subtract \frac{175}{1824} from both sides of the equation.

$$x=\frac{5\sqrt{9092041}-175}{1824} x=\frac{-5\sqrt{9092041}-175}{1824}$$