Solve 4(3x-9)^2-9=7

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{7}{3}, x_{2} = \frac{11}{3}

Alternative Form

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

Evaluate

4 (3 x - 9)^{2} - 9 = 7

Expand the expression

More Steps

Evaluate

4 (3 x - 9)^{2} - 9

Expand the expression

More Steps

Evaluate

4 (3 x - 9)^{2}

Expand the expression

4 (9 x^{2} - 54 x + 81)

Apply the distributive property

4 \times 9 x^{2} - 4 \times 54 x + 4 \times 81

Multiply the numbers

36 x^{2} - 4 \times 54 x + 4 \times 81

Multiply the numbers

36 x^{2} - 216 x + 4 \times 81

Multiply the numbers

36 x^{2} - 216 x + 324

36 x^{2} - 216 x + 324 - 9

Subtract the numbers

36 x^{2} - 216 x + 315

36 x^{2} - 216 x + 315 = 7

Move the expression to the left side

36 x^{2} - 216 x + 308 = 0

Factor the expression

More Steps

Evaluate

36 x^{2} - 216 x + 308

Rewrite the expression

4 \times 9 x^{2} - 4 \times 54 x + 4 \times 77

Factor out 4 from the expression

4 (9 x^{2} - 54 x + 77)

Factor the expression

More Steps

Evaluate

9 x^{2} - 54 x + 77

Rewrite the expression

9 x^{2} + (- 21 - 33) x + 77

Calculate

9 x^{2} - 21 x - 33 x + 77

Rewrite the expression

3 x \times 3 x - 3 x \times 7 - 11 \times 3 x + 11 \times 7

Factor out 3 x from the expression

3 x (3 x - 7) - 11 \times 3 x + 11 \times 7

Factor out - 11 from the expression

3 x (3 x - 7) - 11 (3 x - 7)

Factor out 3 x - 7 from the expression

(3 x - 11) (3 x - 7)

4 (3 x - 11) (3 x - 7)

4 (3 x - 11) (3 x - 7) = 0

Divide the terms

(3 x - 11) (3 x - 7) = 0

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

3 x - 11 = 0 3 x - 7 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 11 = 0

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

3 x = 0 + 11

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

3 x = 11

Divide both sides

\frac{3 x}{3} = \frac{11}{3}

Divide the numbers

x = \frac{11}{3}

x = \frac{11}{3} 3 x - 7 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 7 = 0

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

3 x = 0 + 7

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

3 x = 7

Divide both sides

\frac{3 x}{3} = \frac{7}{3}

Divide the numbers

x = \frac{7}{3}

x = \frac{11}{3} x = \frac{7}{3}

Solution

x_{1} = \frac{7}{3}, x_{2} = \frac{11}{3}

Alternative Form

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

Show Solution

Solve the quadratic equation

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