Solve r^214-16-520

Question

Simplify the expression

14 r^{2} - 536

Evaluate

r^{2} \times 14 - 16 - 520

Use the commutative property to reorder the terms

14 r^{2} - 16 - 520

Solution

14 r^{2} - 536

Show Solution

2 (7 r^{2} - 268)

Evaluate

r^{2} \times 14 - 16 - 520

Use the commutative property to reorder the terms

14 r^{2} - 16 - 520

Subtract the numbers

14 r^{2} - 536

Solution

2 (7 r^{2} - 268)

Show Solution

r_{1} = - \frac{2 469}{7}, r_{2} = \frac{2 469}{7}

Alternative Form

r_{1} \approx - 6.187545, r_{2} \approx 6.187545

Evaluate

r^{2} \times 14 - 16 - 520

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

r^{2} \times 14 - 16 - 520 = 0

Use the commutative property to reorder the terms

14 r^{2} - 16 - 520 = 0

Subtract the numbers

14 r^{2} - 536 = 0

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

14 r^{2} = 0 + 536

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

14 r^{2} = 536

Divide both sides

\frac{14 r ^{2}}{14} = \frac{536}{14}

Divide the numbers

r^{2} = \frac{536}{14}

Cancel out the common factor 2

r^{2} = \frac{268}{7}

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

r = \pm \frac{268}{7}

Simplify the expression

More Steps

Evaluate

\frac{268}{7}

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

\frac{268}{7}

Simplify the radical expression

More Steps

Evaluate

268

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

4 \times 67

Write the number in exponential form with the base of 2

2^{2} \times 67

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

2^{2} \times 67

Reduce the index of the radical and exponent with 2

267

\frac{2 67}{7}

Multiply by the Conjugate

\frac{2 67 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

67 \times 7

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

67 \times 7

Calculate the product

469

\frac{2 469}{7 \times 7}

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

\frac{2 469}{7}

r = \pm \frac{2 469}{7}

Separate the equation into 2 possible cases

r = \frac{2 469}{7} r = - \frac{2 469}{7}

Solution

r_{1} = - \frac{2 469}{7}, r_{2} = \frac{2 469}{7}

Alternative Form

r_{1} \approx - 6.187545, r_{2} \approx 6.187545

Show Solution