Solve 4x^(2)-28x=-45

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{5}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = 2.5, x_{2} = 4.5

Evaluate

4 x^{2} - 28 x = - 45

Move the expression to the left side

4 x^{2} - 28 x + 45 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 28 x + 45

Rewrite the expression

4 x^{2} + (- 10 - 18) x + 45

Calculate

4 x^{2} - 10 x - 18 x + 45

Rewrite the expression

2 x \times 2 x - 2 x \times 5 - 9 \times 2 x + 9 \times 5

Factor out 2 x from the expression

2 x (2 x - 5) - 9 \times 2 x + 9 \times 5

Factor out - 9 from the expression

2 x (2 x - 5) - 9 (2 x - 5)

Factor out 2 x - 5 from the expression

(2 x - 9) (2 x - 5)

(2 x - 9) (2 x - 5) = 0

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

2 x - 9 = 0 2 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 9 = 0

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

2 x = 0 + 9

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

2 x = 9

Divide both sides

\frac{2 x}{2} = \frac{9}{2}

Divide the numbers

x = \frac{9}{2}

x = \frac{9}{2} 2 x - 5 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

\frac{2 x}{2} = \frac{5}{2}

Divide the numbers

x = \frac{5}{2}

x = \frac{9}{2} x = \frac{5}{2}

Solution

x_{1} = \frac{5}{2}, x_{2} = \frac{9}{2}

Alternative Form

x_{1} = 2.5, x_{2} = 4.5

Show Solution