Solve r^2124-1 - ScanMath

Question

Simplify the expression

124 r^{2} - 1

Evaluate

r^{2} \times 124 - 1

Solution

124 r^{2} - 1

Show Solution

r_{1} = - \frac{31}{62}, r_{2} = \frac{31}{62}

Alternative Form

r_{1} \approx - 0.089803, r_{2} \approx 0.089803

Evaluate

r^{2} \times 124 - 1

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

r^{2} \times 124 - 1 = 0

Use the commutative property to reorder the terms

124 r^{2} - 1 = 0

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

124 r^{2} = 0 + 1

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

124 r^{2} = 1

Divide both sides

\frac{124 r ^{2}}{124} = \frac{1}{124}

Divide the numbers

r^{2} = \frac{1}{124}

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

r = \pm \frac{1}{124}

Simplify the expression

More Steps

Evaluate

\frac{1}{124}

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

\frac{1}{124}

Simplify the radical expression

\frac{1}{124}

Simplify the radical expression

More Steps

Evaluate

124

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

4 \times 31

Write the number in exponential form with the base of 2

2^{2} \times 31

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

2^{2} \times 31

Reduce the index of the radical and exponent with 2

231

\frac{1}{2 31}

Multiply by the Conjugate

\frac{31}{2 31 \times 31}

Multiply the numbers

More Steps

Evaluate

231 \times 31

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

2 \times 31

Multiply the terms

62

\frac{31}{62}

r = \pm \frac{31}{62}

Separate the equation into 2 possible cases

r = \frac{31}{62} r = - \frac{31}{62}

Solution

r_{1} = - \frac{31}{62}, r_{2} = \frac{31}{62}

Alternative Form

r_{1} \approx - 0.089803, r_{2} \approx 0.089803

Show Solution