Solve g^2950-20-101

Question

Simplify the expression

950 g^{2} - 121

Evaluate

g^{2} \times 950 - 20 - 101

Use the commutative property to reorder the terms

950 g^{2} - 20 - 101

Solution

950 g^{2} - 121

Show Solution

g_{1} = - \frac{11 38}{190}, g_{2} = \frac{11 38}{190}

Alternative Form

g_{1} \approx - 0.356887, g_{2} \approx 0.356887

Evaluate

g^{2} \times 950 - 20 - 101

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

g^{2} \times 950 - 20 - 101 = 0

Use the commutative property to reorder the terms

950 g^{2} - 20 - 101 = 0

Subtract the numbers

950 g^{2} - 121 = 0

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

950 g^{2} = 0 + 121

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

950 g^{2} = 121

Divide both sides

\frac{950 g ^{2}}{950} = \frac{121}{950}

Divide the numbers

g^{2} = \frac{121}{950}

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

g = \pm \frac{121}{950}

Simplify the expression

More Steps

Evaluate

\frac{121}{950}

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

\frac{121}{950}

Simplify the radical expression

More Steps

Evaluate

121

Write the number in exponential form with the base of 11

1 1^{2}

Reduce the index of the radical and exponent with 2

11

\frac{11}{950}

Simplify the radical expression

More Steps

Evaluate

950

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

25 \times 38

Write the number in exponential form with the base of 5

5^{2} \times 38

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

5^{2} \times 38

Reduce the index of the radical and exponent with 2

538

\frac{11}{5 38}

Multiply by the Conjugate

\frac{11 38}{5 38 \times 38}

Multiply the numbers

More Steps

Evaluate

538 \times 38

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

5 \times 38

Multiply the terms

190

\frac{11 38}{190}

g = \pm \frac{11 38}{190}

Separate the equation into 2 possible cases

g = \frac{11 38}{190} g = - \frac{11 38}{190}

Solution

g_{1} = - \frac{11 38}{190}, g_{2} = \frac{11 38}{190}

Alternative Form

g_{1} \approx - 0.356887, g_{2} \approx 0.356887

Show Solution