Solve -3*10^-14x^2-11^-8x=0

$$-3 \times { 10 }^{ -14 } { x }^{ 2 } - { 11 }^{ -8 } x = 0$$

Solve for x

$$x = -\frac{100000000000000}{643076643} = -155502\frac{295860214}{643076643} \approx -155502.460069911$$

$$x=0$$

Steps Using Factoring

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$-3\times \frac{1}{100000000000000}x^{2}-11^{-8}x=0$$

Multiply -3 and \frac{1}{100000000000000} to get -\frac{3}{100000000000000}.

$$-\frac{3}{100000000000000}x^{2}-11^{-8}x=0$$

Calculate 11 to the power of -8 and get \frac{1}{214358881}.

$$-\frac{3}{100000000000000}x^{2}-\frac{1}{214358881}x=0$$

Factor out x.

$$x\left(-\frac{3}{100000000000000}x-\frac{1}{214358881}\right)=0$$

To find equation solutions, solve x=0 and -\frac{3x}{100000000000000}-\frac{1}{214358881}=0.

$$x=0 x=-\frac{100000000000000}{643076643}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$-3\times \frac{1}{100000000000000}x^{2}-11^{-8}x=0$$

Multiply -3 and \frac{1}{100000000000000} to get -\frac{3}{100000000000000}.

$$-\frac{3}{100000000000000}x^{2}-11^{-8}x=0$$

Calculate 11 to the power of -8 and get \frac{1}{214358881}.

$$-\frac{3}{100000000000000}x^{2}-\frac{1}{214358881}x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{3}{100000000000000} for a, -\frac{1}{214358881} for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{214358881}\right)±\sqrt{\left(-\frac{1}{214358881}\right)^{2}}}{2\left(-\frac{3}{100000000000000}\right)}$$

Take the square root of \left(-\frac{1}{214358881}\right)^{2}.

$$x=\frac{-\left(-\frac{1}{214358881}\right)±\frac{1}{214358881}}{2\left(-\frac{3}{100000000000000}\right)}$$

The opposite of -\frac{1}{214358881} is \frac{1}{214358881}.

$$x=\frac{\frac{1}{214358881}±\frac{1}{214358881}}{2\left(-\frac{3}{100000000000000}\right)}$$

Multiply 2 times -\frac{3}{100000000000000}.

$$x=\frac{\frac{1}{214358881}±\frac{1}{214358881}}{-\frac{3}{50000000000000}}$$

Now solve the equation x=\frac{\frac{1}{214358881}±\frac{1}{214358881}}{-\frac{3}{50000000000000}} when ± is plus. Add \frac{1}{214358881} to \frac{1}{214358881} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{\frac{2}{214358881}}{-\frac{3}{50000000000000}}$$

Divide \frac{2}{214358881} by -\frac{3}{50000000000000} by multiplying \frac{2}{214358881} by the reciprocal of -\frac{3}{50000000000000}.

$$x=-\frac{100000000000000}{643076643}$$

Now solve the equation x=\frac{\frac{1}{214358881}±\frac{1}{214358881}}{-\frac{3}{50000000000000}} when ± is minus. Subtract \frac{1}{214358881} from \frac{1}{214358881} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0}{-\frac{3}{50000000000000}}$$

Divide 0 by -\frac{3}{50000000000000} by multiplying 0 by the reciprocal of -\frac{3}{50000000000000}.

$$x=0$$

The equation is now solved.

$$x=-\frac{100000000000000}{643076643} x=0$$

Steps for Completing the Square

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$-3\times \frac{1}{100000000000000}x^{2}-11^{-8}x=0$$

Multiply -3 and \frac{1}{100000000000000} to get -\frac{3}{100000000000000}.

$$-\frac{3}{100000000000000}x^{2}-11^{-8}x=0$$

Calculate 11 to the power of -8 and get \frac{1}{214358881}.

$$-\frac{3}{100000000000000}x^{2}-\frac{1}{214358881}x=0$$

Divide both sides of the equation by -\frac{3}{100000000000000}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{-\frac{3}{100000000000000}x^{2}-\frac{1}{214358881}x}{-\frac{3}{100000000000000}}=\frac{0}{-\frac{3}{100000000000000}}$$

Dividing by -\frac{3}{100000000000000} undoes the multiplication by -\frac{3}{100000000000000}.

$$x^{2}+\left(-\frac{\frac{1}{214358881}}{-\frac{3}{100000000000000}}\right)x=\frac{0}{-\frac{3}{100000000000000}}$$

Divide -\frac{1}{214358881} by -\frac{3}{100000000000000} by multiplying -\frac{1}{214358881} by the reciprocal of -\frac{3}{100000000000000}.

$$x^{2}+\frac{100000000000000}{643076643}x=\frac{0}{-\frac{3}{100000000000000}}$$

Divide 0 by -\frac{3}{100000000000000} by multiplying 0 by the reciprocal of -\frac{3}{100000000000000}.

$$x^{2}+\frac{100000000000000}{643076643}x=0$$

Divide \frac{100000000000000}{643076643}, the coefficient of the x term, by 2 to get \frac{50000000000000}{643076643}. Then add the square of \frac{50000000000000}{643076643} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{100000000000000}{643076643}x+\left(\frac{50000000000000}{643076643}\right)^{2}=\left(\frac{50000000000000}{643076643}\right)^{2}$$

Square \frac{50000000000000}{643076643} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{100000000000000}{643076643}x+\frac{2500000000000000000000000000}{413547568772149449}=\frac{2500000000000000000000000000}{413547568772149449}$$

Factor x^{2}+\frac{100000000000000}{643076643}x+\frac{2500000000000000000000000000}{413547568772149449}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{50000000000000}{643076643}\right)^{2}=\frac{2500000000000000000000000000}{413547568772149449}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{50000000000000}{643076643}\right)^{2}}=\sqrt{\frac{2500000000000000000000000000}{413547568772149449}}$$

Simplify.

$$x+\frac{50000000000000}{643076643}=\frac{50000000000000}{643076643} x+\frac{50000000000000}{643076643}=-\frac{50000000000000}{643076643}$$

Subtract \frac{50000000000000}{643076643} from both sides of the equation.

$$x=0 x=-\frac{100000000000000}{643076643}$$