Solve 25(x-1)^2=49

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{2}{5}, x_{2} = \frac{12}{5}

Alternative Form

x_{1} = - 0.4, x_{2} = 2.4

Evaluate

25 (x - 1)^{2} = 49

Expand the expression

More Steps

Evaluate

25 (x - 1)^{2}

Expand the expression

More Steps

Evaluate

(x - 1)^{2}

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

x^{2} - 2 x \times 1 + 1^{2}

Calculate

x^{2} - 2 x + 1

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

Apply the distributive property

25 x^{2} - 25 \times 2 x + 25 \times 1

Multiply the numbers

25 x^{2} - 50 x + 25 \times 1

Any expression multiplied by 1 remains the same

25 x^{2} - 50 x + 25

25 x^{2} - 50 x + 25 = 49

Move the expression to the left side

25 x^{2} - 50 x - 24 = 0

Factor the expression

More Steps

Evaluate

25 x^{2} - 50 x - 24

Rewrite the expression

25 x^{2} + (10 - 60) x - 24

Calculate

25 x^{2} + 10 x - 60 x - 24

Rewrite the expression

5 x \times 5 x + 5 x \times 2 - 12 \times 5 x - 12 \times 2

Factor out 5 x from the expression

5 x (5 x + 2) - 12 \times 5 x - 12 \times 2

Factor out - 12 from the expression

5 x (5 x + 2) - 12 (5 x + 2)

Factor out 5 x + 2 from the expression

(5 x - 12) (5 x + 2)

(5 x - 12) (5 x + 2) = 0

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

5 x - 12 = 0 5 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 12 = 0

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

5 x = 0 + 12

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

5 x = 12

Divide both sides

\frac{5 x}{5} = \frac{12}{5}

Divide the numbers

x = \frac{12}{5}

x = \frac{12}{5} 5 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 2 = 0

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

5 x = 0 - 2

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

5 x = - 2

Divide both sides

\frac{5 x}{5} = \frac{- 2}{5}

Divide the numbers

x = \frac{- 2}{5}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{2}{5}

x = \frac{12}{5} x = - \frac{2}{5}

Solution

x_{1} = - \frac{2}{5}, x_{2} = \frac{12}{5}

Alternative Form

x_{1} = - 0.4, x_{2} = 2.4

Show Solution