Solve 4(x-2)^2=25

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 0.5, x_{2} = 4.5

Evaluate

4 (x - 2)^{2} = 25

Expand the expression

More Steps

Evaluate

4 (x - 2)^{2}

Expand the expression

More Steps

Evaluate

(x - 2)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

x^{2} - 2 x \times 2 + 2^{2}

Calculate

x^{2} - 4 x + 4

4 (x^{2} - 4 x + 4)

Apply the distributive property

4 x^{2} - 4 \times 4 x + 4 \times 4

Multiply the numbers

4 x^{2} - 16 x + 4 \times 4

Multiply the numbers

4 x^{2} - 16 x + 16

4 x^{2} - 16 x + 16 = 25

Move the expression to the left side

4 x^{2} - 16 x - 9 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 16 x - 9

Rewrite the expression

4 x^{2} + (2 - 18) x - 9

Calculate

4 x^{2} + 2 x - 18 x - 9

Rewrite the expression

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

Factor out 2 x from the expression

2 x (2 x + 1) - 9 \times 2 x - 9

Factor out - 9 from the expression

2 x (2 x + 1) - 9 (2 x + 1)

Factor out 2 x + 1 from the expression

(2 x - 9) (2 x + 1)

(2 x - 9) (2 x + 1) = 0

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

2 x - 9 = 0 2 x + 1 = 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 + 1 = 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}

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

x = - \frac{1}{2}

x = \frac{9}{2} x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 4.5

Show Solution