Solve 8a4a-1 - ScanMath

Question

Simplify the expression

32 a^{2} - 1

Evaluate

8 a \times 4 a - 1

Solution

More Steps

Evaluate

8 a \times 4 a

Multiply the terms

32 a \times a

Multiply the terms

32 a^{2}

32 a^{2} - 1

Show Solution

a_{1} = - \frac{2}{8}, a_{2} = \frac{2}{8}

Alternative Form

a_{1} \approx - 0.176777, a_{2} \approx 0.176777

Evaluate

8 a \times 4 a - 1

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

8 a \times 4 a - 1 = 0

Multiply

More Steps

Multiply the terms

8 a \times 4 a

Multiply the terms

32 a \times a

Multiply the terms

32 a^{2}

32 a^{2} - 1 = 0

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

32 a^{2} = 0 + 1

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

32 a^{2} = 1

Divide both sides

\frac{32 a ^{2}}{32} = \frac{1}{32}

Divide the numbers

a^{2} = \frac{1}{32}

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

a = \pm \frac{1}{32}

Simplify the expression

More Steps

Evaluate

\frac{1}{32}

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

\frac{1}{32}

Simplify the radical expression

\frac{1}{32}

Simplify the radical expression

More Steps

Evaluate

32

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

16 \times 2

Write the number in exponential form with the base of 4

4^{2} \times 2

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

4^{2} \times 2

Reduce the index of the radical and exponent with 2

42

\frac{1}{4 2}

Multiply by the Conjugate

\frac{2}{4 2 \times 2}

Multiply the numbers

More Steps

Evaluate

42 \times 2

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

4 \times 2

Multiply the terms

8

\frac{2}{8}

a = \pm \frac{2}{8}

Separate the equation into 2 possible cases

a = \frac{2}{8} a = - \frac{2}{8}

Solution

a_{1} = - \frac{2}{8}, a_{2} = \frac{2}{8}

Alternative Form

a_{1} \approx - 0.176777, a_{2} \approx 0.176777

Show Solution