Solve 16p^(2 ) - 24p + 5= 0

Question

Solve the quadratic equation

p_{1} = \frac{1}{4}, p_{2} = \frac{5}{4}

Alternative Form

p_{1} = 0.25, p_{2} = 1.25

Evaluate

16 p^{2} - 24 p + 5 = 0

Factor the expression

More Steps

Evaluate

16 p^{2} - 24 p + 5

Rewrite the expression

16 p^{2} + (- 4 - 20) p + 5

Calculate

16 p^{2} - 4 p - 20 p + 5

Rewrite the expression

4 p \times 4 p - 4 p - 5 \times 4 p + 5

Factor out 4 p from the expression

4 p (4 p - 1) - 5 \times 4 p + 5

Factor out - 5 from the expression

4 p (4 p - 1) - 5 (4 p - 1)

Factor out 4 p - 1 from the expression

(4 p - 5) (4 p - 1)

(4 p - 5) (4 p - 1) = 0

When the product of factors equals 0,at least one factor is 0

4 p - 5 = 0 4 p - 1 = 0

Solve the equation for p

More Steps

Evaluate

4 p - 5 = 0

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

4 p = 0 + 5

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

4 p = 5

Divide both sides

\frac{4 p}{4} = \frac{5}{4}

Divide the numbers

p = \frac{5}{4}

p = \frac{5}{4} 4 p - 1 = 0

Solve the equation for p

More Steps

Evaluate

4 p - 1 = 0

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

4 p = 0 + 1

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

4 p = 1

Divide both sides

\frac{4 p}{4} = \frac{1}{4}

Divide the numbers

p = \frac{1}{4}

p = \frac{5}{4} p = \frac{1}{4}

Solution

p_{1} = \frac{1}{4}, p_{2} = \frac{5}{4}

Alternative Form

p_{1} = 0.25, p_{2} = 1.25

Show Solution