Solve 2b^2 -5b = 3

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

b_{1} = - 0.5, b_{2} = 3

Evaluate

2 b^{2} - 5 b = 3

Move the expression to the left side

2 b^{2} - 5 b - 3 = 0

Factor the expression

More Steps

Evaluate

2 b^{2} - 5 b - 3

Rewrite the expression

2 b^{2} + (1 - 6) b - 3

Calculate

2 b^{2} + b - 6 b - 3

Rewrite the expression

b \times 2 b + b - 3 \times 2 b - 3

Factor out b from the expression

b (2 b + 1) - 3 \times 2 b - 3

Factor out - 3 from the expression

b (2 b + 1) - 3 (2 b + 1)

Factor out 2 b + 1 from the expression

(b - 3) (2 b + 1)

(b - 3) (2 b + 1) = 0

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

b - 3 = 0 2 b + 1 = 0

Solve the equation for b

More Steps

Evaluate

b - 3 = 0

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

b = 0 + 3

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

b = 3

b = 3 2 b + 1 = 0

Solve the equation for b

More Steps

Evaluate

2 b + 1 = 0

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

2 b = 0 - 1

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

2 b = - 1

Divide both sides

\frac{2 b}{2} = \frac{- 1}{2}

Divide the numbers

b = \frac{- 1}{2}

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

b = - \frac{1}{2}

b = 3 b = - \frac{1}{2}

Solution

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

Alternative Form

b_{1} = - 0.5, b_{2} = 3

Show Solution