Solve 1/7(3x-5)^2=28

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 3, x_{2} = \frac{19}{3}

Alternative Form

x_{1} = - 3, x_{2} = 6. \dot{3}

Evaluate

\frac{1}{7} (3 x - 5)^{2} = 28

Expand the expression

More Steps

Evaluate

\frac{1}{7} (3 x - 5)^{2}

Expand the expression

More Steps

Evaluate

(3 x - 5)^{2}

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

(3 x)^{2} - 2 \times 3 x \times 5 + 5^{2}

Calculate

9 x^{2} - 30 x + 25

\frac{1}{7} (9 x^{2} - 30 x + 25)

Apply the distributive property

\frac{1}{7} \times 9 x^{2} - \frac{1}{7} \times 30 x + \frac{1}{7} \times 25

Multiply the numbers

\frac{9}{7} x^{2} - \frac{1}{7} \times 30 x + \frac{1}{7} \times 25

Multiply the numbers

\frac{9}{7} x^{2} - \frac{30}{7} x + \frac{1}{7} \times 25

Multiply the numbers

\frac{9}{7} x^{2} - \frac{30}{7} x + \frac{25}{7}

\frac{9}{7} x^{2} - \frac{30}{7} x + \frac{25}{7} = 28

Move the expression to the left side

\frac{9}{7} x^{2} - \frac{30}{7} x - \frac{171}{7} = 0

Factor the expression

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Evaluate

\frac{9}{7} x^{2} - \frac{30}{7} x - \frac{171}{7}

Rewrite the expression

\frac{3}{7} \times 3 x^{2} - \frac{3}{7} \times 10 x - \frac{3}{7} \times 57

Factor out \frac{3}{7} from the expression

\frac{3}{7} (3 x^{2} - 10 x - 57)

Factor the expression

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Evaluate

3 x^{2} - 10 x - 57

Rewrite the expression

3 x^{2} + (- 19 + 9) x - 57

Calculate

3 x^{2} - 19 x + 9 x - 57

Rewrite the expression

x \times 3 x - x \times 19 + 3 \times 3 x - 3 \times 19

Factor out x from the expression

x (3 x - 19) + 3 \times 3 x - 3 \times 19

Factor out 3 from the expression

x (3 x - 19) + 3 (3 x - 19)

Factor out 3 x - 19 from the expression

(x + 3) (3 x - 19)

\frac{3}{7} (x + 3) (3 x - 19)

\frac{3}{7} (x + 3) (3 x - 19) = 0

Divide the terms

(x + 3) (3 x - 19) = 0

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

3 x - 19 = 0 x + 3 = 0

Solve the equation for x

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Evaluate

3 x - 19 = 0

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

3 x = 0 + 19

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

3 x = 19

Divide both sides

\frac{3 x}{3} = \frac{19}{3}

Divide the numbers

x = \frac{19}{3}

x = \frac{19}{3} x + 3 = 0

Solve the equation for x

More Steps

Evaluate

x + 3 = 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 = \frac{19}{3} x = - 3

Solution

x_{1} = - 3, x_{2} = \frac{19}{3}

Alternative Form

x_{1} = - 3, x_{2} = 6. \dot{3}

Show Solution