Solve x(2x+5)=3 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

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

Evaluate

x (2 x + 5) = 3

Expand the expression

More Steps

Evaluate

x (2 x + 5)

Apply the distributive property

x \times 2 x + x \times 5

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} + x \times 5

Use the commutative property to reorder the terms

2 x^{2} + 5 x

2 x^{2} + 5 x = 3

Move the expression to the left side

2 x^{2} + 5 x - 3 = 0

Factor the expression

More Steps

Evaluate

2 x^{2} + 5 x - 3

Rewrite the expression

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

Calculate

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

Rewrite the expression

x \times 2 x - x + 3 \times 2 x - 3

Factor out x from the expression

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

Factor out 3 from the expression

x (2 x - 1) + 3 (2 x - 1)

Factor out 2 x - 1 from the expression

(x + 3) (2 x - 1)

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

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

2 x - 1 = 0 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 1 = 0

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

2 x = 0 + 1

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

2 x = 1

Divide both sides

\frac{2 x}{2} = \frac{1}{2}

Divide the numbers

x = \frac{1}{2}

x = \frac{1}{2} x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 3 = 0

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

x = 0 - 3

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

x = - 3

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

Solution

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

Alternative Form

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

Show Solution