Solve 4(x-1)^2-81=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{7}{2}, x_{2} = \frac{11}{2}

Alternative Form

x_{1} = - 3.5, x_{2} = 5.5

Evaluate

4 (x - 1)^{2} - 81 = 0

Expand the expression

More Steps

Evaluate

4 (x - 1)^{2} - 81

Expand the expression

More Steps

Evaluate

4 (x - 1)^{2}

Expand the expression

4 (x^{2} - 2 x + 1)

Apply the distributive property

4 x^{2} - 4 \times 2 x + 4 \times 1

Multiply the numbers

4 x^{2} - 8 x + 4 \times 1

Any expression multiplied by 1 remains the same

4 x^{2} - 8 x + 4

4 x^{2} - 8 x + 4 - 81

Subtract the numbers

4 x^{2} - 8 x - 77

4 x^{2} - 8 x - 77 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 8 x - 77

Rewrite the expression

4 x^{2} + (14 - 22) x - 77

Calculate

4 x^{2} + 14 x - 22 x - 77

Rewrite the expression

2 x \times 2 x + 2 x \times 7 - 11 \times 2 x - 11 \times 7

Factor out 2 x from the expression

2 x (2 x + 7) - 11 \times 2 x - 11 \times 7

Factor out - 11 from the expression

2 x (2 x + 7) - 11 (2 x + 7)

Factor out 2 x + 7 from the expression

(2 x - 11) (2 x + 7)

(2 x - 11) (2 x + 7) = 0

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

2 x - 11 = 0 2 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 11 = 0

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

2 x = 0 + 11

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

2 x = 11

Divide both sides

\frac{2 x}{2} = \frac{11}{2}

Divide the numbers

x = \frac{11}{2}

x = \frac{11}{2} 2 x + 7 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 7 = 0

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

2 x = 0 - 7

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

2 x = - 7

Divide both sides

\frac{2 x}{2} = \frac{- 7}{2}

Divide the numbers

x = \frac{- 7}{2}

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

x = - \frac{7}{2}

x = \frac{11}{2} x = - \frac{7}{2}

Solution

x_{1} = - \frac{7}{2}, x_{2} = \frac{11}{2}

Alternative Form

x_{1} = - 3.5, x_{2} = 5.5

Show Solution