Solve (7x-8)(x-2)=13

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{1}{7}, x_{2} = 3

Alternative Form

x_{1} = 0. \dot{1} 4285 \dot{7}, x_{2} = 3

Evaluate

(7 x - 8) (x - 2) = 13

Expand the expression

More Steps

Evaluate

(7 x - 8) (x - 2)

Apply the distributive property

7 x \times x - 7 x \times 2 - 8 x - (- 8 \times 2)

Multiply the terms

7 x^{2} - 7 x \times 2 - 8 x - (- 8 \times 2)

Multiply the numbers

7 x^{2} - 14 x - 8 x - (- 8 \times 2)

Multiply the numbers

7 x^{2} - 14 x - 8 x - (- 16)

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

7 x^{2} - 14 x - 8 x + 16

Subtract the terms

More Steps

Evaluate

- 14 x - 8 x

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

(- 14 - 8) x

Subtract the numbers

- 22 x

7 x^{2} - 22 x + 16

7 x^{2} - 22 x + 16 = 13

Move the expression to the left side

7 x^{2} - 22 x + 3 = 0

Factor the expression

More Steps

Evaluate

7 x^{2} - 22 x + 3

Rewrite the expression

7 x^{2} + (- 1 - 21) x + 3

Calculate

7 x^{2} - x - 21 x + 3

Rewrite the expression

x \times 7 x - x - 3 \times 7 x + 3

Factor out x from the expression

x (7 x - 1) - 3 \times 7 x + 3

Factor out - 3 from the expression

x (7 x - 1) - 3 (7 x - 1)

Factor out 7 x - 1 from the expression

(x - 3) (7 x - 1)

(x - 3) (7 x - 1) = 0

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

x - 3 = 0 7 x - 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 3 = 0

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

x = 0 + 3

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

x = 3

x = 3 7 x - 1 = 0

Solve the equation for x

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 = 3 x = \frac{1}{7}

Solution

x_{1} = \frac{1}{7}, x_{2} = 3

Alternative Form

x_{1} = 0. \dot{1} 4285 \dot{7}, x_{2} = 3

Show Solution

Solve the quadratic equation

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