Solve 15b^2-8b-3=-4

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

b_{1} = \frac{1}{5}, b_{2} = \frac{1}{3}

Alternative Form

b_{1} = 0.2, b_{2} = 0. \dot{3}

Evaluate

15 b^{2} - 8 b - 3 = - 4

Move the expression to the left side

15 b^{2} - 8 b + 1 = 0

Factor the expression

More Steps

Evaluate

15 b^{2} - 8 b + 1

Rewrite the expression

15 b^{2} + (- 3 - 5) b + 1

Calculate

15 b^{2} - 3 b - 5 b + 1

Rewrite the expression

3 b \times 5 b - 3 b - 5 b + 1

Factor out 3 b from the expression

3 b (5 b - 1) - 5 b + 1

Factor out - 1 from the expression

3 b (5 b - 1) - (5 b - 1)

Factor out 5 b - 1 from the expression

(3 b - 1) (5 b - 1)

(3 b - 1) (5 b - 1) = 0

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

3 b - 1 = 0 5 b - 1 = 0

Solve the equation for b

More Steps

Evaluate

3 b - 1 = 0

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

3 b = 0 + 1

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

3 b = 1

Divide both sides

\frac{3 b}{3} = \frac{1}{3}

Divide the numbers

b = \frac{1}{3}

b = \frac{1}{3} 5 b - 1 = 0

Solve the equation for b

More Steps

Evaluate

5 b - 1 = 0

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

5 b = 0 + 1

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

5 b = 1

Divide both sides

\frac{5 b}{5} = \frac{1}{5}

Divide the numbers

b = \frac{1}{5}

b = \frac{1}{3} b = \frac{1}{5}

Solution

b_{1} = \frac{1}{5}, b_{2} = \frac{1}{3}

Alternative Form

b_{1} = 0.2, b_{2} = 0. \dot{3}

Show Solution