Solve (x-5)^2-25 - ScanMath

Question

Simplify the expression

x^{2} - 10 x

Evaluate

(x - 5)^{2} - 25

Expand the expression

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

Solution

x^{2} - 10 x

Show Solution

(x - 10) x

Evaluate

(x - 5)^{2} - 25

Rewrite the expression in exponential form

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

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

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

Evaluate

(x - 10) (x - 5 + 5)

Solution

(x - 10) x

Show Solution

x_{1} = 0, x_{2} = 10

Evaluate

(x - 5)^{2} - 25

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

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

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

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

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

(x - 5)^{2} = 25

Take the root of both sides of the equation and remember to use both positive and negative roots

x - 5 = \pm 25

Simplify the expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

x - 5 = \pm 5

Separate the equation into 2 possible cases

x - 5 = 5 x - 5 = - 5

Calculate

More Steps

Evaluate

x - 5 = 5

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

x = 5 + 5

Add the numbers

x = 10

x = 10 x - 5 = - 5

Calculate

More Steps

Evaluate

x - 5 = - 5

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

x = - 5 + 5

Add the numbers

x = 0

x = 10 x = 0

Solution

x_{1} = 0, x_{2} = 10

Show Solution