Solve 25(1-4x)^(2)-28=-12

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{1}{20}, x_{2} = \frac{9}{20}

Alternative Form

x_{1} = 0.05, x_{2} = 0.45

Evaluate

25 (1 - 4 x)^{2} - 28 = - 12

Expand the expression

More Steps

Evaluate

25 (1 - 4 x)^{2} - 28

Expand the expression

More Steps

Evaluate

25 (1 - 4 x)^{2}

Expand the expression

25 (1 - 8 x + 16 x^{2})

Apply the distributive property

25 \times 1 - 25 \times 8 x + 25 \times 16 x^{2}

Any expression multiplied by 1 remains the same

25 - 25 \times 8 x + 25 \times 16 x^{2}

Multiply the numbers

25 - 200 x + 25 \times 16 x^{2}

Multiply the numbers

25 - 200 x + 400 x^{2}

25 - 200 x + 400 x^{2} - 28

Subtract the numbers

- 3 - 200 x + 400 x^{2}

- 3 - 200 x + 400 x^{2} = - 12

Move the expression to the left side

9 - 200 x + 400 x^{2} = 0

Factor the expression

More Steps

Evaluate

9 - 200 x + 400 x^{2}

Rewrite the expression

9 + (- 180 - 20) x + 400 x^{2}

Calculate

9 - 180 x - 20 x + 400 x^{2}

Rewrite the expression

9 - 9 \times 20 x - 20 x + 20 x \times 20 x

Factor out 9 from the expression

9 (1 - 20 x) - 20 x + 20 x \times 20 x

Factor out - 20 x from the expression

9 (1 - 20 x) - 20 x (1 - 20 x)

Factor out 1 - 20 x from the expression

(9 - 20 x) (1 - 20 x)

(9 - 20 x) (1 - 20 x) = 0

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

9 - 20 x = 0 1 - 20 x = 0

Solve the equation for x

More Steps

Evaluate

9 - 20 x = 0

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

- 20 x = 0 - 9

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

- 20 x = - 9

Change the signs on both sides of the equation

20 x = 9

Divide both sides

\frac{20 x}{20} = \frac{9}{20}

Divide the numbers

x = \frac{9}{20}

x = \frac{9}{20} 1 - 20 x = 0

Solve the equation for x

More Steps

Evaluate

1 - 20 x = 0

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

- 20 x = 0 - 1

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

- 20 x = - 1

Change the signs on both sides of the equation

20 x = 1

Divide both sides

\frac{20 x}{20} = \frac{1}{20}

Divide the numbers

x = \frac{1}{20}

x = \frac{9}{20} x = \frac{1}{20}

Solution

x_{1} = \frac{1}{20}, x_{2} = \frac{9}{20}

Alternative Form

x_{1} = 0.05, x_{2} = 0.45

Show Solution