Solve 4z^2 -4z-15=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

z_{1} = - \frac{3}{2}, z_{2} = \frac{5}{2}

Alternative Form

z_{1} = - 1.5, z_{2} = 2.5

Evaluate

4 z^{2} - 4 z - 15 = 0

Factor the expression

More Steps

Evaluate

4 z^{2} - 4 z - 15

Rewrite the expression

4 z^{2} + (6 - 10) z - 15

Calculate

4 z^{2} + 6 z - 10 z - 15

Rewrite the expression

2 z \times 2 z + 2 z \times 3 - 5 \times 2 z - 5 \times 3

Factor out 2 z from the expression

2 z (2 z + 3) - 5 \times 2 z - 5 \times 3

Factor out - 5 from the expression

2 z (2 z + 3) - 5 (2 z + 3)

Factor out 2 z + 3 from the expression

(2 z - 5) (2 z + 3)

(2 z - 5) (2 z + 3) = 0

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

2 z - 5 = 0 2 z + 3 = 0

Solve the equation for z

More Steps

Evaluate

2 z - 5 = 0

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

2 z = 0 + 5

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

2 z = 5

Divide both sides

\frac{2 z}{2} = \frac{5}{2}

Divide the numbers

z = \frac{5}{2}

z = \frac{5}{2} 2 z + 3 = 0

Solve the equation for z

More Steps

Evaluate

2 z + 3 = 0

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

2 z = 0 - 3

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

2 z = - 3

Divide both sides

\frac{2 z}{2} = \frac{- 3}{2}

Divide the numbers

z = \frac{- 3}{2}

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

z = - \frac{3}{2}

z = \frac{5}{2} z = - \frac{3}{2}

Solution

z_{1} = - \frac{3}{2}, z_{2} = \frac{5}{2}

Alternative Form

z_{1} = - 1.5, z_{2} = 2.5

Show Solution