What are the solutions to the equation 10^{-14}=(4*10^{-8}+x)x ?

The solutions to the equation 10^{-14}=(4*10^{-8}+x)x are x=0,x=-1/25000000

Find the zeros of 10^{-14}=(4*10^{-8}+x)x

The zeros of 10^{-14}=(4*10^{-8}+x)x are x=0,x=-1/25000000

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1 0^{- 14} = (4 \cdot 1 0^{- 8} + x) x

x = 0, x = - \frac{1}{25000000}

Decimal Notation

x = 0, x = - 0.00000004

Solution steps

1 0^{- 14} = (4 \cdot 1 0^{- 8} + x) x

Expand

1 0^{- 14} : \frac{1}{1 0 ^{14}}

Expand

(4 \cdot 1 0^{- 8} + x) x : \frac{1}{25000000} x + x^{2}

\frac{1}{1 0 ^{14}} = \frac{1}{25000000} x + x^{2}

Switch sides

\frac{1}{25000000} x + x^{2} = \frac{1}{1 0 ^{14}}

Move

\frac{1}{1 0 ^{14}}

to the left side

\frac{1}{25000000} x + x^{2} - \frac{1}{1 0 ^{14}} = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} + \frac{1 \cdot x}{25000000} = 0

Factor

x^{2} + \frac{1 \cdot x}{25000000} : x (x + \frac{1}{25000000})

x (x + \frac{1}{25000000}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or x + \frac{1}{25000000} = 0

Solve

x + \frac{1}{25000000} = 0 : x = - \frac{1}{25000000}

The solutions to the quadratic equation are:

x = 0, x = - \frac{1}{25000000}

2 x^{2} + 6 x + 6 > - 9 x - 1

- 3 = 5.475 t + 0.5 (- 9.8) t^{2}

4 x^{2} + 16 x y - 9 y^{2}

∣ - 6 + x ∣ = 4

\frac{2}{3} x + 3 = 1

What are the solutions to the equation 10^{-14}=(4*10^{-8}+x)x ?
The solutions to the equation 10^{-14}=(4*10^{-8}+x)x are x=0,x=-1/25000000
Find the zeros of 10^{-14}=(4*10^{-8}+x)x
The zeros of 10^{-14}=(4*10^{-8}+x)x are x=0,x=-1/25000000