Solve p^232-9 - ScanMath

Question

Simplify the expression

32 p^{2} - 9

Evaluate

p^{2} \times 32 - 9

Solution

32 p^{2} - 9

Show Solution

p_{1} = - \frac{3 2}{8}, p_{2} = \frac{3 2}{8}

Alternative Form

p_{1} \approx - 0.53033, p_{2} \approx 0.53033

Evaluate

p^{2} \times 32 - 9

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

p^{2} \times 32 - 9 = 0

Use the commutative property to reorder the terms

32 p^{2} - 9 = 0

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

32 p^{2} = 0 + 9

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

32 p^{2} = 9

Divide both sides

\frac{32 p ^{2}}{32} = \frac{9}{32}

Divide the numbers

p^{2} = \frac{9}{32}

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

p = \pm \frac{9}{32}

Simplify the expression

More Steps

Evaluate

\frac{9}{32}

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

\frac{9}{32}

Simplify the radical expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

\frac{3}{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{3}{4 2}

Multiply by the Conjugate

\frac{3 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{3 2}{8}

p = \pm \frac{3 2}{8}

Separate the equation into 2 possible cases

p = \frac{3 2}{8} p = - \frac{3 2}{8}

Solution

p_{1} = - \frac{3 2}{8}, p_{2} = \frac{3 2}{8}

Alternative Form

p_{1} \approx - 0.53033, p_{2} \approx 0.53033

Show Solution