Solve (7x - 1)(5x - 1)

Question

Simplify the expression

35 x^{2} - 12 x + 1

Evaluate

(7 x - 1) (5 x - 1)

Apply the distributive property

7 x \times 5 x - 7 x \times 1 - 5 x - (- 1)

Multiply the terms

More Steps

Evaluate

7 x \times 5 x

Multiply the numbers

35 x \times x

Multiply the terms

35 x^{2}

35 x^{2} - 7 x \times 1 - 5 x - (- 1)

Any expression multiplied by 1 remains the same

35 x^{2} - 7 x - 5 x - (- 1)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

35 x^{2} - 7 x - 5 x + 1

Solution

More Steps

Evaluate

- 7 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(- 7 - 5) x

Subtract the numbers

- 12 x

35 x^{2} - 12 x + 1

Show Solution

Find the roots

x_{1} = \frac{1}{7}, x_{2} = \frac{1}{5}

Alternative Form

x_{1} = 0. \dot{1} 4285 \dot{7}, x_{2} = 0.2

Evaluate

(7 x - 1) (5 x - 1)

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

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

Separate the equation into 2 possible cases

7 x - 1 = 0 5 x - 1 = 0

Solve the equation

More Steps

Evaluate

7 x - 1 = 0

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

7 x = 0 + 1

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

7 x = 1

Divide both sides

\frac{7 x}{7} = \frac{1}{7}

Divide the numbers

x = \frac{1}{7}

x = \frac{1}{7} 5 x - 1 = 0

Solve the equation

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{1}{7} x = \frac{1}{5}

Solution

x_{1} = \frac{1}{7}, x_{2} = \frac{1}{5}

Alternative Form

x_{1} = 0. \dot{1} 4285 \dot{7}, x_{2} = 0.2

Show Solution