Solve x^2 - 2x + 6 = x(2x - 7)

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 1, x_{2} = 6

Evaluate

x^{2} - 2 x + 6 = x (2 x - 7)

Expand the expression

More Steps

Evaluate

x (2 x - 7)

Apply the distributive property

x \times 2 x - x \times 7

Multiply the terms

More Steps

Evaluate

x \times 2 x

Use the commutative property to reorder the terms

2 x \times x

Multiply the terms

2 x^{2}

2 x^{2} - x \times 7

Use the commutative property to reorder the terms

2 x^{2} - 7 x

x^{2} - 2 x + 6 = 2 x^{2} - 7 x

Move the expression to the left side

- x^{2} + 5 x + 6 = 0

Factor the expression

More Steps

Evaluate

- x^{2} + 5 x + 6

Rewrite the expression

- x^{2} + (- 1 + 6) x + 6

Calculate

- x^{2} - x + 6 x + 6

Rewrite the expression

- x \times x - x + 6 x + 6

Factor out - x from the expression

- x (x + 1) + 6 x + 6

Factor out 6 from the expression

- x (x + 1) + 6 (x + 1)

Factor out x + 1 from the expression

(- x + 6) (x + 1)

(- x + 6) (x + 1) = 0

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

- x + 6 = 0 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

- x + 6 = 0

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

- x = 0 - 6

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

- x = - 6

Change the signs on both sides of the equation

x = 6

x = 6 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = 6 x = - 1

Solution

x_{1} = - 1, x_{2} = 6

Show Solution