Solve 39210-2g^240

Question

Simplify the expression

39210 - 80 g^{2}

Evaluate

39210 - 2 g^{2} \times 40

Solution

39210 - 80 g^{2}

Show Solution

10 (3921 - 8 g^{2})

Evaluate

39210 - 2 g^{2} \times 40

Multiply the terms

39210 - 80 g^{2}

Solution

10 (3921 - 8 g^{2})

Show Solution

g_{1} = - \frac{7842}{4}, g_{2} = \frac{7842}{4}

Alternative Form

g_{1} \approx - 22.138767, g_{2} \approx 22.138767

Evaluate

39210 - 2 g^{2} \times 40

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

39210 - 2 g^{2} \times 40 = 0

Multiply the terms

39210 - 80 g^{2} = 0

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

- 80 g^{2} = 0 - 39210

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

- 80 g^{2} = - 39210

Change the signs on both sides of the equation

80 g^{2} = 39210

Divide both sides

\frac{80 g ^{2}}{80} = \frac{39210}{80}

Divide the numbers

g^{2} = \frac{39210}{80}

Cancel out the common factor 10

g^{2} = \frac{3921}{8}

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

g = \pm \frac{3921}{8}

Simplify the expression

More Steps

Evaluate

\frac{3921}{8}

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

\frac{3921}{8}

Simplify the radical expression

More Steps

Evaluate

8

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

The root of a product is equal to the product of the roots of each factor

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{3921}{2 2}

Multiply by the Conjugate

\frac{3921 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

3921 \times 2

The product of roots with the same index is equal to the root of the product

3921 \times 2

Calculate the product

7842

\frac{7842}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{7842}{4}

g = \pm \frac{7842}{4}

Separate the equation into 2 possible cases

g = \frac{7842}{4} g = - \frac{7842}{4}

Solution

g_{1} = - \frac{7842}{4}, g_{2} = \frac{7842}{4}

Alternative Form

g_{1} \approx - 22.138767, g_{2} \approx 22.138767

Show Solution