Solve n^2-1-3/8 - ScanMath

Question

Simplify the expression

n^{2} - \frac{11}{8}

Evaluate

n^{2} - 1 - \frac{3}{8}

Solution

More Steps

Evaluate

- 1 - \frac{3}{8}

Reduce fractions to a common denominator

- \frac{8}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{- 8 - 3}{8}

Subtract the numbers

\frac{- 11}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{11}{8}

n^{2} - \frac{11}{8}

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Factor the expression

\frac{1}{8} (8 n^{2} - 11)

Evaluate

n^{2} - 1 - \frac{3}{8}

Subtract the numbers

More Steps

Evaluate

- 1 - \frac{3}{8}

Reduce fractions to a common denominator

- \frac{8}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{- 8 - 3}{8}

Subtract the numbers

\frac{- 11}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{11}{8}

n^{2} - \frac{11}{8}

Solution

\frac{1}{8} (8 n^{2} - 11)

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Find the roots

n_{1} = - \frac{22}{4}, n_{2} = \frac{22}{4}

Alternative Form

n_{1} \approx - 1.172604, n_{2} \approx 1.172604

Evaluate

n^{2} - 1 - \frac{3}{8}

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

n^{2} - 1 - \frac{3}{8} = 0

Subtract the numbers

More Steps

Simplify

n^{2} - 1 - \frac{3}{8}

Subtract the numbers

More Steps

Evaluate

- 1 - \frac{3}{8}

Reduce fractions to a common denominator

- \frac{8}{8} - \frac{3}{8}

Write all numerators above the common denominator

\frac{- 8 - 3}{8}

Subtract the numbers

\frac{- 11}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{11}{8}

n^{2} - \frac{11}{8}

n^{2} - \frac{11}{8} = 0

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

n^{2} = 0 + \frac{11}{8}

Add the terms

n^{2} = \frac{11}{8}

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

n = \pm \frac{11}{8}

Simplify the expression

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Evaluate

\frac{11}{8}

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

\frac{11}{8}

Simplify the radical expression

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Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{11}{2 2}

Multiply by the Conjugate

\frac{11 \times 2}{2 2 \times 2}

Multiply the numbers

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Evaluate

11 \times 2

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

11 \times 2

Calculate the product

22

\frac{22}{2 2 \times 2}

Multiply the numbers

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Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{22}{4}

n = \pm \frac{22}{4}

Separate the equation into 2 possible cases

n = \frac{22}{4} n = - \frac{22}{4}

Solution

n_{1} = - \frac{22}{4}, n_{2} = \frac{22}{4}

Alternative Form

n_{1} \approx - 1.172604, n_{2} \approx 1.172604

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