Solve 2x-7=(x-3)^2-4

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Evaluate

2 x - 7 = (x - 3)^{2} - 4

Swap the sides

(x - 3)^{2} - 4 = 2 x - 7

Expand the expression

More Steps

Evaluate

(x - 3)^{2} - 4

Expand the expression

More Steps

Evaluate

(x - 3)^{2}

Use (a - b)^{2} = a^{2} - 2 ab + b^{2} to expand the expression

x^{2} - 2 x \times 3 + 3^{2}

Calculate

x^{2} - 6 x + 9

x^{2} - 6 x + 9 - 4

Subtract the numbers

x^{2} - 6 x + 5

x^{2} - 6 x + 5 = 2 x - 7

Move the expression to the left side

x^{2} - 8 x + 12 = 0

Factor the expression

More Steps

Evaluate

x^{2} - 8 x + 12

Rewrite the expression

x^{2} + (- 2 - 6) x + 12

Calculate

x^{2} - 2 x - 6 x + 12

Rewrite the expression

x \times x - x \times 2 - 6 x + 6 \times 2

Factor out x from the expression

x (x - 2) - 6 x + 6 \times 2

Factor out - 6 from the expression

x (x - 2) - 6 (x - 2)

Factor out x - 2 from the expression

(x - 6) (x - 2)

(x - 6) (x - 2) = 0

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

x - 6 = 0 x - 2 = 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

x = 6 x - 2 = 0

Solve the equation for x

More Steps

Evaluate

x - 2 = 0

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

x = 0 + 2

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

x = 2

x = 6 x = 2

Solution

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

Show Solution