Solve 1430-24g^24

Question

Simplify the expression

1430 - 96 g^{2}

Evaluate

1430 - 24 g^{2} \times 4

Solution

1430 - 96 g^{2}

Show Solution

2 (715 - 48 g^{2})

Evaluate

1430 - 24 g^{2} \times 4

Multiply the terms

1430 - 96 g^{2}

Solution

2 (715 - 48 g^{2})

Show Solution

g_{1} = - \frac{2145}{12}, g_{2} = \frac{2145}{12}

Alternative Form

g_{1} \approx - 3.859512, g_{2} \approx 3.859512

Evaluate

1430 - 24 g^{2} \times 4

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

1430 - 24 g^{2} \times 4 = 0

Multiply the terms

1430 - 96 g^{2} = 0

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

- 96 g^{2} = 0 - 1430

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

- 96 g^{2} = - 1430

Change the signs on both sides of the equation

96 g^{2} = 1430

Divide both sides

\frac{96 g ^{2}}{96} = \frac{1430}{96}

Divide the numbers

g^{2} = \frac{1430}{96}

Cancel out the common factor 2

g^{2} = \frac{715}{48}

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

g = \pm \frac{715}{48}

Simplify the expression

More Steps

Evaluate

\frac{715}{48}

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

\frac{715}{48}

Simplify the radical expression

More Steps

Evaluate

48

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

16 \times 3

Write the number in exponential form with the base of 4

4^{2} \times 3

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

4^{2} \times 3

Reduce the index of the radical and exponent with 2

43

\frac{715}{4 3}

Multiply by the Conjugate

\frac{715 \times 3}{4 3 \times 3}

Multiply the numbers

More Steps

Evaluate

715 \times 3

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

715 \times 3

Calculate the product

2145

\frac{2145}{4 3 \times 3}

Multiply the numbers

More Steps

Evaluate

43 \times 3

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

4 \times 3

Multiply the terms

12

\frac{2145}{12}

g = \pm \frac{2145}{12}

Separate the equation into 2 possible cases

g = \frac{2145}{12} g = - \frac{2145}{12}

Solution

g_{1} = - \frac{2145}{12}, g_{2} = \frac{2145}{12}

Alternative Form

g_{1} \approx - 3.859512, g_{2} \approx 3.859512

Show Solution