Solve l^214-36 - ScanMath

Question

Simplify the expression

14 l^{2} - 36

Evaluate

l^{2} \times 14 - 36

Solution

14 l^{2} - 36

Show Solution

2 (7 l^{2} - 18)

Evaluate

l^{2} \times 14 - 36

Use the commutative property to reorder the terms

14 l^{2} - 36

Solution

2 (7 l^{2} - 18)

Show Solution

l_{1} = - \frac{3 14}{7}, l_{2} = \frac{3 14}{7}

Alternative Form

l_{1} \approx - 1.603567, l_{2} \approx 1.603567

Evaluate

l^{2} \times 14 - 36

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

l^{2} \times 14 - 36 = 0

Use the commutative property to reorder the terms

14 l^{2} - 36 = 0

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

14 l^{2} = 0 + 36

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

14 l^{2} = 36

Divide both sides

\frac{14 l ^{2}}{14} = \frac{36}{14}

Divide the numbers

l^{2} = \frac{36}{14}

Cancel out the common factor 2

l^{2} = \frac{18}{7}

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

l = \pm \frac{18}{7}

Simplify the expression

More Steps

Evaluate

\frac{18}{7}

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

\frac{18}{7}

Simplify the radical expression

More Steps

Evaluate

18

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

9 \times 2

Write the number in exponential form with the base of 3

3^{2} \times 2

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

3^{2} \times 2

Reduce the index of the radical and exponent with 2

32

\frac{3 2}{7}

Multiply by the Conjugate

\frac{3 2 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

2 \times 7

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

2 \times 7

Calculate the product

14

\frac{3 14}{7 \times 7}

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

\frac{3 14}{7}

l = \pm \frac{3 14}{7}

Separate the equation into 2 possible cases

l = \frac{3 14}{7} l = - \frac{3 14}{7}

Solution

l_{1} = - \frac{3 14}{7}, l_{2} = \frac{3 14}{7}

Alternative Form

l_{1} \approx - 1.603567, l_{2} \approx 1.603567

Show Solution