Solve w 12 w -8 w = 15

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

w_{1} = - \frac{5}{6}, w_{2} = \frac{3}{2}

Alternative Form

w_{1} = - 0.8 \dot{3}, w_{2} = 1.5

Evaluate

w \times 12 w - 8 w = 15

Multiply

More Steps

Evaluate

w \times 12 w

Multiply the terms

w^{2} \times 12

Use the commutative property to reorder the terms

12 w^{2}

12 w^{2} - 8 w = 15

Move the expression to the left side

12 w^{2} - 8 w - 15 = 0

Factor the expression

More Steps

Evaluate

12 w^{2} - 8 w - 15

Rewrite the expression

12 w^{2} + (10 - 18) w - 15

Calculate

12 w^{2} + 10 w - 18 w - 15

Rewrite the expression

2 w \times 6 w + 2 w \times 5 - 3 \times 6 w - 3 \times 5

Factor out 2 w from the expression

2 w (6 w + 5) - 3 \times 6 w - 3 \times 5

Factor out - 3 from the expression

2 w (6 w + 5) - 3 (6 w + 5)

Factor out 6 w + 5 from the expression

(2 w - 3) (6 w + 5)

(2 w - 3) (6 w + 5) = 0

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

2 w - 3 = 0 6 w + 5 = 0

Solve the equation for w

More Steps

Evaluate

2 w - 3 = 0

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

2 w = 0 + 3

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

2 w = 3

Divide both sides

\frac{2 w}{2} = \frac{3}{2}

Divide the numbers

w = \frac{3}{2}

w = \frac{3}{2} 6 w + 5 = 0

Solve the equation for w

More Steps

Evaluate

6 w + 5 = 0

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

6 w = 0 - 5

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

6 w = - 5

Divide both sides

\frac{6 w}{6} = \frac{- 5}{6}

Divide the numbers

w = \frac{- 5}{6}

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

w = - \frac{5}{6}

w = \frac{3}{2} w = - \frac{5}{6}

Solution

w_{1} = - \frac{5}{6}, w_{2} = \frac{3}{2}

Alternative Form

w_{1} = - 0.8 \dot{3}, w_{2} = 1.5

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