Solve l^2414-1 - ScanMath

Question

Simplify the expression

414 l^{2} - 1

Evaluate

l^{2} \times 414 - 1

Solution

414 l^{2} - 1

Show Solution

l_{1} = - \frac{46}{138}, l_{2} = \frac{46}{138}

Alternative Form

l_{1} \approx - 0.049147, l_{2} \approx 0.049147

Evaluate

l^{2} \times 414 - 1

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

l^{2} \times 414 - 1 = 0

Use the commutative property to reorder the terms

414 l^{2} - 1 = 0

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

414 l^{2} = 0 + 1

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

414 l^{2} = 1

Divide both sides

\frac{414 l ^{2}}{414} = \frac{1}{414}

Divide the numbers

l^{2} = \frac{1}{414}

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

l = \pm \frac{1}{414}

Simplify the expression

More Steps

Evaluate

\frac{1}{414}

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

\frac{1}{414}

Simplify the radical expression

\frac{1}{414}

Simplify the radical expression

More Steps

Evaluate

414

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

9 \times 46

Write the number in exponential form with the base of 3

3^{2} \times 46

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

3^{2} \times 46

Reduce the index of the radical and exponent with 2

346

\frac{1}{3 46}

Multiply by the Conjugate

\frac{46}{3 46 \times 46}

Multiply the numbers

More Steps

Evaluate

346 \times 46

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

3 \times 46

Multiply the terms

138

\frac{46}{138}

l = \pm \frac{46}{138}

Separate the equation into 2 possible cases

l = \frac{46}{138} l = - \frac{46}{138}

Solution

l_{1} = - \frac{46}{138}, l_{2} = \frac{46}{138}

Alternative Form

l_{1} \approx - 0.049147, l_{2} \approx 0.049147

Show Solution