Solve 31500-152g^2

Question

Factor the expression

4 (7875 - 38 g^{2})

Evaluate

31500 - 152 g^{2}

Solution

4 (7875 - 38 g^{2})

Show Solution

g_{1} = - \frac{15 1330}{38}, g_{2} = \frac{15 1330}{38}

Alternative Form

g_{1} \approx - 14.395723, g_{2} \approx 14.395723

Evaluate

31500 - 152 g^{2}

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

31500 - 152 g^{2} = 0

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

- 152 g^{2} = 0 - 31500

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

- 152 g^{2} = - 31500

Change the signs on both sides of the equation

152 g^{2} = 31500

Divide both sides

\frac{152 g ^{2}}{152} = \frac{31500}{152}

Divide the numbers

g^{2} = \frac{31500}{152}

Cancel out the common factor 4

g^{2} = \frac{7875}{38}

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

g = \pm \frac{7875}{38}

Simplify the expression

More Steps

Evaluate

\frac{7875}{38}

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

\frac{7875}{38}

Simplify the radical expression

More Steps

Evaluate

7875

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

225 \times 35

Write the number in exponential form with the base of 15

1 5^{2} \times 35

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

1 5^{2} \times 35

Reduce the index of the radical and exponent with 2

1535

\frac{15 35}{38}

Multiply by the Conjugate

\frac{15 35 \times 38}{38 \times 38}

Multiply the numbers

More Steps

Evaluate

35 \times 38

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

35 \times 38

Calculate the product

1330

\frac{15 1330}{38 \times 38}

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

\frac{15 1330}{38}

g = \pm \frac{15 1330}{38}

Separate the equation into 2 possible cases

g = \frac{15 1330}{38} g = - \frac{15 1330}{38}

Solution

g_{1} = - \frac{15 1330}{38}, g_{2} = \frac{15 1330}{38}

Alternative Form

g_{1} \approx - 14.395723, g_{2} \approx 14.395723

Show Solution