Solve 5(5x-6)^(2)-27=18

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{3}{5}, x_{2} = \frac{9}{5}

Alternative Form

x_{1} = 0.6, x_{2} = 1.8

Evaluate

5 (5 x - 6)^{2} - 27 = 18

Expand the expression

More Steps

Evaluate

5 (5 x - 6)^{2} - 27

Expand the expression

More Steps

Evaluate

5 (5 x - 6)^{2}

Expand the expression

5 (25 x^{2} - 60 x + 36)

Apply the distributive property

5 \times 25 x^{2} - 5 \times 60 x + 5 \times 36

Multiply the numbers

125 x^{2} - 5 \times 60 x + 5 \times 36

Multiply the numbers

125 x^{2} - 300 x + 5 \times 36

Multiply the numbers

125 x^{2} - 300 x + 180

125 x^{2} - 300 x + 180 - 27

Subtract the numbers

125 x^{2} - 300 x + 153

125 x^{2} - 300 x + 153 = 18

Move the expression to the left side

125 x^{2} - 300 x + 135 = 0

Factor the expression

More Steps

Evaluate

125 x^{2} - 300 x + 135

Rewrite the expression

5 \times 25 x^{2} - 5 \times 60 x + 5 \times 27

Factor out 5 from the expression

5 (25 x^{2} - 60 x + 27)

Factor the expression

More Steps

Evaluate

25 x^{2} - 60 x + 27

Rewrite the expression

25 x^{2} + (- 15 - 45) x + 27

Calculate

25 x^{2} - 15 x - 45 x + 27

Rewrite the expression

5 x \times 5 x - 5 x \times 3 - 9 \times 5 x + 9 \times 3

Factor out 5 x from the expression

5 x (5 x - 3) - 9 \times 5 x + 9 \times 3

Factor out - 9 from the expression

5 x (5 x - 3) - 9 (5 x - 3)

Factor out 5 x - 3 from the expression

(5 x - 9) (5 x - 3)

5 (5 x - 9) (5 x - 3)

5 (5 x - 9) (5 x - 3) = 0

Divide the terms

(5 x - 9) (5 x - 3) = 0

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

5 x - 9 = 0 5 x - 3 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 9 = 0

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

5 x = 0 + 9

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

5 x = 9

Divide both sides

\frac{5 x}{5} = \frac{9}{5}

Divide the numbers

x = \frac{9}{5}

x = \frac{9}{5} 5 x - 3 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 3 = 0

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

5 x = 0 + 3

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

5 x = 3

Divide both sides

\frac{5 x}{5} = \frac{3}{5}

Divide the numbers

x = \frac{3}{5}

x = \frac{9}{5} x = \frac{3}{5}

Solution

x_{1} = \frac{3}{5}, x_{2} = \frac{9}{5}

Alternative Form

x_{1} = 0.6, x_{2} = 1.8

Show Solution

Solve the quadratic equation

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