Solve 25x^2-25x+4

Question

Factor the expression

(5 x - 4) (5 x - 1)

Evaluate

25 x^{2} - 25 x + 4

Rewrite the expression

25 x^{2} + (- 5 - 20) x + 4

Calculate

25 x^{2} - 5 x - 20 x + 4

Rewrite the expression

5 x \times 5 x - 5 x - 4 \times 5 x + 4

Factor out 5 x from the expression

5 x (5 x - 1) - 4 \times 5 x + 4

Factor out - 4 from the expression

5 x (5 x - 1) - 4 (5 x - 1)

Solution

(5 x - 4) (5 x - 1)

Show Solution

x_{1} = \frac{1}{5}, x_{2} = \frac{4}{5}

Alternative Form

x_{1} = 0.2, x_{2} = 0.8

Evaluate

25 x^{2} - 25 x + 4

To find the roots of the expression,set the expression equal to 0

25 x^{2} - 25 x + 4 = 0

Factor the expression

More Steps

Evaluate

25 x^{2} - 25 x + 4

Rewrite the expression

25 x^{2} + (- 5 - 20) x + 4

Calculate

25 x^{2} - 5 x - 20 x + 4

Rewrite the expression

5 x \times 5 x - 5 x - 4 \times 5 x + 4

Factor out 5 x from the expression

5 x (5 x - 1) - 4 \times 5 x + 4

Factor out - 4 from the expression

5 x (5 x - 1) - 4 (5 x - 1)

Factor out 5 x - 1 from the expression

(5 x - 4) (5 x - 1)

(5 x - 4) (5 x - 1) = 0

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

5 x - 4 = 0 5 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 4 = 0

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

5 x = 0 + 4

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

5 x = 4

Divide both sides

\frac{5 x}{5} = \frac{4}{5}

Divide the numbers

x = \frac{4}{5}

x = \frac{4}{5} 5 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 1 = 0

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

5 x = 0 + 1

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

5 x = 1

Divide both sides

\frac{5 x}{5} = \frac{1}{5}

Divide the numbers

x = \frac{1}{5}

x = \frac{4}{5} x = \frac{1}{5}

Solution

x_{1} = \frac{1}{5}, x_{2} = \frac{4}{5}

Alternative Form

x_{1} = 0.2, x_{2} = 0.8

Show Solution