Solve (1.25)(-25)^2=50(10)^3x^2

$$( 1.25 ) ( - 25 ) ^ { 2 } = 50 ( 10 ) ^ { 3 } x ^ { 2 }$$

Solve for x

$$x=0.125$$

$$x=-0.125$$

Steps by Finding Square Root

Calculate -25 to the power of 2 and get 625.

$$1.25\times 625=50\times 10^{3}x^{2}$$

Multiply 1.25 and 625 to get 781.25.

$$781.25=50\times 10^{3}x^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$781.25=50\times 1000x^{2}$$

Multiply 50 and 1000 to get 50000.

$$781.25=50000x^{2}$$

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

$$50000x^{2}=781.25$$

Divide both sides by 50000.

$$x^{2}=\frac{781.25}{50000}$$

Expand \frac{781.25}{50000} by multiplying both numerator and the denominator by 100.

$$x^{2}=\frac{78125}{5000000}$$

Reduce the fraction \frac{78125}{5000000} to lowest terms by extracting and canceling out 78125.

$$x^{2}=\frac{1}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{1}{8} x=-\frac{1}{8}$$

Steps Using the Quadratic Formula

Calculate -25 to the power of 2 and get 625.

$$1.25\times 625=50\times 10^{3}x^{2}$$

Multiply 1.25 and 625 to get 781.25.

$$781.25=50\times 10^{3}x^{2}$$

Calculate 10 to the power of 3 and get 1000.

$$781.25=50\times 1000x^{2}$$

Multiply 50 and 1000 to get 50000.

$$781.25=50000x^{2}$$

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

$$50000x^{2}=781.25$$

Subtract 781.25 from both sides.

$$50000x^{2}-781.25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 50000 for a, 0 for b, and -781.25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 50000\left(-781.25\right)}}{2\times 50000}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 50000\left(-781.25\right)}}{2\times 50000}$$

Multiply -4 times 50000.

$$x=\frac{0±\sqrt{-200000\left(-781.25\right)}}{2\times 50000}$$

Multiply -200000 times -781.25.

$$x=\frac{0±\sqrt{156250000}}{2\times 50000}$$

Take the square root of 156250000.

$$x=\frac{0±12500}{2\times 50000}$$

Multiply 2 times 50000.

$$x=\frac{0±12500}{100000}$$

Now solve the equation x=\frac{0±12500}{100000} when ± is plus. Reduce the fraction \frac{12500}{100000} to lowest terms by extracting and canceling out 12500.

$$x=\frac{1}{8}$$

Now solve the equation x=\frac{0±12500}{100000} when ± is minus. Reduce the fraction \frac{-12500}{100000} to lowest terms by extracting and canceling out 12500.

$$x=-\frac{1}{8}$$

The equation is now solved.

$$x=\frac{1}{8} x=-\frac{1}{8}$$