Solve -7g=3g 8(-g^2)

Question

Solve the equation

g_{1} = - \frac{42}{12}, g_{2} = 0, g_{3} = \frac{42}{12}

Alternative Form

g_{1} \approx - 0.540062, g_{2} = 0, g_{3} \approx 0.540062

Evaluate

- 7 g = 3 g \times 8 (- g^{2})

Multiply

More Steps

Evaluate

3 g \times 8 (- g^{2})

Any expression multiplied by 1 remains the same

- 3 g \times 8 g^{2}

Multiply the terms

- 24 g \times g^{2}

Multiply the terms with the same base by adding their exponents

- 24 g^{1 + 2}

Add the numbers

- 24 g^{3}

- 7 g = - 24 g^{3}

Add or subtract both sides

- 7 g - (- 24 g^{3}) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 7 g + 24 g^{3} = 0

Factor the expression

g (- 7 + 24 g^{2}) = 0

Separate the equation into 2 possible cases

g = 0 - 7 + 24 g^{2} = 0

Solve the equation

More Steps

Evaluate

- 7 + 24 g^{2} = 0

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

24 g^{2} = 0 + 7

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

24 g^{2} = 7

Divide both sides

\frac{24 g ^{2}}{24} = \frac{7}{24}

Divide the numbers

g^{2} = \frac{7}{24}

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

g = \pm \frac{7}{24}

Simplify the expression

More Steps

Evaluate

\frac{7}{24}

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

\frac{7}{24}

Simplify the radical expression

\frac{7}{2 6}

Multiply by the Conjugate

\frac{7 \times 6}{2 6 \times 6}

Multiply the numbers

\frac{42}{2 6 \times 6}

Multiply the numbers

\frac{42}{12}

g = \pm \frac{42}{12}

Separate the equation into 2 possible cases

g = \frac{42}{12} g = - \frac{42}{12}

g = 0 g = \frac{42}{12} g = - \frac{42}{12}

Solution

g_{1} = - \frac{42}{12}, g_{2} = 0, g_{3} = \frac{42}{12}

Alternative Form

g_{1} \approx - 0.540062, g_{2} = 0, g_{3} \approx 0.540062

Show Solution

Solve the equation

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