Solve e-2226g e^2324g

Question

Simplify the expression

e - 721224 e^{2} g^{2}

Evaluate

e - 2226 g e^{2} \times 324 g

Solution

More Steps

Evaluate

2226 g e^{2} \times 324 g

Multiply the terms

721224 g e^{2} g

Multiply the terms

721224 g^{2} e^{2}

Multiply the numbers

721224 e^{2} g^{2}

e - 721224 e^{2} g^{2}

Show Solution

Factor the expression

e (1 - 721224 e g^{2})

Evaluate

e - 2226 g e^{2} \times 324 g

Multiply

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Evaluate

2226 g e^{2} \times 324 g

Multiply the terms

721224 g e^{2} g

Multiply the terms

721224 g^{2} e^{2}

Multiply the numbers

721224 e^{2} g^{2}

e - 721224 e^{2} g^{2}

Solution

e (1 - 721224 e g^{2})

Show Solution

Find the roots

g_{1} = - \frac{2226 e}{40068 e}, g_{2} = \frac{2226 e}{40068 e}

Alternative Form

g_{1} \approx - 0.000714, g_{2} \approx 0.000714

Evaluate

e - 2226 g e^{2} \times 324 g

To find the roots of the expression,set the expression equal to 0

e - 2226 g e^{2} \times 324 g = 0

Multiply

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Multiply the terms

2226 g e^{2} \times 324 g

Multiply the terms

721224 g e^{2} g

Multiply the terms

721224 g^{2} e^{2}

Multiply the numbers

721224 e^{2} g^{2}

e - 721224 e^{2} g^{2} = 0

Move the constant to the right-hand side and change its sign

- 721224 e^{2} g^{2} = 0 - e

Removing 0 doesn't change the value,so remove it from the expression

- 721224 e^{2} g^{2} = - e

Change the signs on both sides of the equation

721224 e^{2} g^{2} = e

Divide both sides

\frac{721224 e ^{2} g ^{2}}{721224 e ^{2}} = \frac{e}{721224 e ^{2}}

Divide the numbers

g^{2} = \frac{e}{721224 e ^{2}}

Divide the numbers

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Evaluate

\frac{e}{e ^{2}}

Use the product rule \frac{a ^{n}}{a ^{m}} = a^{n - m} to simplify the expression

\frac{1}{e ^{2 - 1}}

Subtract the terms

\frac{1}{e ^{1}}

Simplify

\frac{1}{e}

g^{2} = \frac{1}{721224 e}

Take the root of both sides of the equation and remember to use both positive and negative roots

g = \pm \frac{1}{721224 e}

Simplify the expression

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Evaluate

\frac{1}{721224 e}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{721224 e}

Simplify the radical expression

\frac{1}{721224 e}

Simplify the radical expression

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Evaluate

721224 e

Rewrite the expression

721224 \times e

Simplify the root

18 2226 e

\frac{1}{18 2226 e}

Multiply by the Conjugate

\frac{2226 e}{18 2226 e \times 2226 e}

Multiply the numbers

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Evaluate

18 2226 e \times 2226 e

When a square root of an expression is multiplied by itself,the result is that expression

18 \times 2226 e

Multiply the terms

40068 e

\frac{2226 e}{40068 e}

g = \pm \frac{2226 e}{40068 e}

Separate the equation into 2 possible cases

g = \frac{2226 e}{40068 e} g = - \frac{2226 e}{40068 e}

Solution

g_{1} = - \frac{2226 e}{40068 e}, g_{2} = \frac{2226 e}{40068 e}

Alternative Form

g_{1} \approx - 0.000714, g_{2} \approx 0.000714

Show Solution