Solve r^2316-1 - ScanMath

Question

Simplify the expression

316 r^{2} - 1

Evaluate

r^{2} \times 316 - 1

Solution

316 r^{2} - 1

Show Solution

r_{1} = - \frac{79}{158}, r_{2} = \frac{79}{158}

Alternative Form

r_{1} \approx - 0.056254, r_{2} \approx 0.056254

Evaluate

r^{2} \times 316 - 1

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

r^{2} \times 316 - 1 = 0

Use the commutative property to reorder the terms

316 r^{2} - 1 = 0

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

316 r^{2} = 0 + 1

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

316 r^{2} = 1

Divide both sides

\frac{316 r ^{2}}{316} = \frac{1}{316}

Divide the numbers

r^{2} = \frac{1}{316}

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

r = \pm \frac{1}{316}

Simplify the expression

More Steps

Evaluate

\frac{1}{316}

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

\frac{1}{316}

Simplify the radical expression

\frac{1}{316}

Simplify the radical expression

More Steps

Evaluate

316

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

4 \times 79

Write the number in exponential form with the base of 2

2^{2} \times 79

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

2^{2} \times 79

Reduce the index of the radical and exponent with 2

279

\frac{1}{2 79}

Multiply by the Conjugate

\frac{79}{2 79 \times 79}

Multiply the numbers

More Steps

Evaluate

279 \times 79

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

2 \times 79

Multiply the terms

158

\frac{79}{158}

r = \pm \frac{79}{158}

Separate the equation into 2 possible cases

r = \frac{79}{158} r = - \frac{79}{158}

Solution

r_{1} = - \frac{79}{158}, r_{2} = \frac{79}{158}

Alternative Form

r_{1} \approx - 0.056254, r_{2} \approx 0.056254

Show Solution