Solve 2(x-5)-x^2+25=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 3, x_{2} = 5

Evaluate

2 (x - 5) - x^{2} + 25 = 0

Expand the expression

More Steps

Evaluate

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

Multiply the terms

More Steps

Evaluate

2 (x - 5)

Apply the distributive property

2 x - 2 \times 5

Multiply the numbers

2 x - 10

2 x - 10 - x^{2} + 25

Add the numbers

2 x + 15 - x^{2}

2 x + 15 - x^{2} = 0

Factor the expression

More Steps

Evaluate

2 x + 15 - x^{2}

Reorder the terms

15 + 2 x - x^{2}

Rewrite the expression

15 + (5 - 3) x - x^{2}

Calculate

15 + 5 x - 3 x - x^{2}

Rewrite the expression

5 \times 3 + 5 x - x \times 3 - x \times x

Factor out 5 from the expression

5 (3 + x) - x \times 3 - x \times x

Factor out - x from the expression

5 (3 + x) - x (3 + x)

Factor out 3 + x from the expression

(5 - x) (3 + x)

(5 - x) (3 + x) = 0

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

5 - x = 0 3 + x = 0

Solve the equation for x

More Steps

Evaluate

5 - x = 0

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

- x = 0 - 5

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

- x = - 5

Change the signs on both sides of the equation

x = 5

x = 5 3 + x = 0

Solve the equation for x

More Steps

Evaluate

3 + x = 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 = 5 x = - 3

Solution

x_{1} = - 3, x_{2} = 5

Show Solution