Solve 0.64=9*10^5*1.5625*10^-12-x^2/0.64

$$0.64 = 9 \times 10 ^ { 5 } \times \frac { 1.5625 \times 10 ^ { - 12 } - x ^ { 2 } } { 0.64 }$$

Solve for x (complex solution)

$$x=-\frac{i\sqrt{2621431}}{2400000}\approx -0-0.000674618i$$

$$x=\frac{i\sqrt{2621431}}{2400000}\approx 0.000674618i$$

Steps by Finding Square Root

Calculate 10 to the power of 5 and get 100000.

$$0.64=9\times 100000\times \frac{1.5625\times 10^{-12}-x^{2}}{0.64}$$

Multiply 9 and 100000 to get 900000.

$$0.64=900000\times \frac{1.5625\times 10^{-12}-x^{2}}{0.64}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$0.64=900000\times \frac{1.5625\times \frac{1}{1000000000000}-x^{2}}{0.64}$$

Multiply 1.5625 and \frac{1}{1000000000000} to get \frac{1}{640000000000}.

$$0.64=900000\times \frac{\frac{1}{640000000000}-x^{2}}{0.64}$$

Divide each term of \frac{1}{640000000000}-x^{2} by 0.64 to get \frac{\frac{1}{640000000000}}{0.64}+\frac{-x^{2}}{0.64}.

$$0.64=900000\left(\frac{\frac{1}{640000000000}}{0.64}+\frac{-x^{2}}{0.64}\right)$$

Express \frac{\frac{1}{640000000000}}{0.64} as a single fraction.

$$0.64=900000\left(\frac{1}{640000000000\times 0.64}+\frac{-x^{2}}{0.64}\right)$$

Multiply 640000000000 and 0.64 to get 409600000000.

$$0.64=900000\left(\frac{1}{409600000000}+\frac{-x^{2}}{0.64}\right)$$

Divide -x^{2} by 0.64 to get -1.5625x^{2}.

$$0.64=900000\left(\frac{1}{409600000000}-1.5625x^{2}\right)$$

Use the distributive property to multiply 900000 by \frac{1}{409600000000}-1.5625x^{2}.

$$0.64=\frac{9}{4096000}-1406250x^{2}$$

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

$$\frac{9}{4096000}-1406250x^{2}=0.64$$

Subtract \frac{9}{4096000} from both sides.

$$-1406250x^{2}=0.64-\frac{9}{4096000}$$

Subtract \frac{9}{4096000} from 0.64 to get \frac{2621431}{4096000}.

$$-1406250x^{2}=\frac{2621431}{4096000}$$

Divide both sides by -1406250.

$$x^{2}=\frac{\frac{2621431}{4096000}}{-1406250}$$

Express \frac{\frac{2621431}{4096000}}{-1406250} as a single fraction.

$$x^{2}=\frac{2621431}{4096000\left(-1406250\right)}$$

Multiply 4096000 and -1406250 to get -5760000000000.

$$x^{2}=\frac{2621431}{-5760000000000}$$

Fraction \frac{2621431}{-5760000000000} can be rewritten as -\frac{2621431}{5760000000000} by extracting the negative sign.

$$x^{2}=-\frac{2621431}{5760000000000}$$

The equation is now solved.

$$x=\frac{\sqrt{2621431}i}{2400000} x=-\frac{\sqrt{2621431}i}{2400000}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of 5 and get 100000.

$$0.64=9\times 100000\times \frac{1.5625\times 10^{-12}-x^{2}}{0.64}$$

Multiply 9 and 100000 to get 900000.

$$0.64=900000\times \frac{1.5625\times 10^{-12}-x^{2}}{0.64}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$0.64=900000\times \frac{1.5625\times \frac{1}{1000000000000}-x^{2}}{0.64}$$

Multiply 1.5625 and \frac{1}{1000000000000} to get \frac{1}{640000000000}.

$$0.64=900000\times \frac{\frac{1}{640000000000}-x^{2}}{0.64}$$

Divide each term of \frac{1}{640000000000}-x^{2} by 0.64 to get \frac{\frac{1}{640000000000}}{0.64}+\frac{-x^{2}}{0.64}.

$$0.64=900000\left(\frac{\frac{1}{640000000000}}{0.64}+\frac{-x^{2}}{0.64}\right)$$

Express \frac{\frac{1}{640000000000}}{0.64} as a single fraction.

$$0.64=900000\left(\frac{1}{640000000000\times 0.64}+\frac{-x^{2}}{0.64}\right)$$

Multiply 640000000000 and 0.64 to get 409600000000.

$$0.64=900000\left(\frac{1}{409600000000}+\frac{-x^{2}}{0.64}\right)$$

Divide -x^{2} by 0.64 to get -1.5625x^{2}.

$$0.64=900000\left(\frac{1}{409600000000}-1.5625x^{2}\right)$$

Use the distributive property to multiply 900000 by \frac{1}{409600000000}-1.5625x^{2}.

$$0.64=\frac{9}{4096000}-1406250x^{2}$$

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

$$\frac{9}{4096000}-1406250x^{2}=0.64$$

Subtract 0.64 from both sides.

$$\frac{9}{4096000}-1406250x^{2}-0.64=0$$

Subtract 0.64 from \frac{9}{4096000} to get -\frac{2621431}{4096000}.

$$-\frac{2621431}{4096000}-1406250x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-1406250x^{2}-\frac{2621431}{4096000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1406250 for a, 0 for b, and -\frac{2621431}{4096000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1406250\right)\left(-\frac{2621431}{4096000}\right)}}{2\left(-1406250\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1406250\right)\left(-\frac{2621431}{4096000}\right)}}{2\left(-1406250\right)}$$

Multiply -4 times -1406250.

$$x=\frac{0±\sqrt{5625000\left(-\frac{2621431}{4096000}\right)}}{2\left(-1406250\right)}$$

Multiply 5625000 times -\frac{2621431}{4096000}.

$$x=\frac{0±\sqrt{-\frac{14745549375}{4096}}}{2\left(-1406250\right)}$$

Take the square root of -\frac{14745549375}{4096}.

$$x=\frac{0±\frac{75\sqrt{2621431}i}{64}}{2\left(-1406250\right)}$$

Multiply 2 times -1406250.

$$x=\frac{0±\frac{75\sqrt{2621431}i}{64}}{-2812500}$$

Now solve the equation x=\frac{0±\frac{75\sqrt{2621431}i}{64}}{-2812500} when ± is plus.

$$x=-\frac{\sqrt{2621431}i}{2400000}$$

Now solve the equation x=\frac{0±\frac{75\sqrt{2621431}i}{64}}{-2812500} when ± is minus.

$$x=\frac{\sqrt{2621431}i}{2400000}$$

The equation is now solved.

$$x=-\frac{\sqrt{2621431}i}{2400000} x=\frac{\sqrt{2621431}i}{2400000}$$