Solve -9(x-10)^2=-4

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = \frac{28}{3}, x_{2} = \frac{32}{3}

Alternative Form

x_{1} = 9. \dot{3}, x_{2} = 10. \dot{6}

Evaluate

- 9 (x - 10)^{2} = - 4

Expand the expression

More Steps

Evaluate

- 9 (x - 10)^{2}

Expand the expression

More Steps

Evaluate

(x - 10)^{2}

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

x^{2} - 2 x \times 10 + 1 0^{2}

Calculate

x^{2} - 20 x + 100

- 9 (x^{2} - 20 x + 100)

Apply the distributive property

- 9 x^{2} - (- 9 \times 20 x) - 9 \times 100

Multiply the numbers

- 9 x^{2} - (- 180 x) - 9 \times 100

Multiply the numbers

- 9 x^{2} - (- 180 x) - 900

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 9 x^{2} + 180 x - 900

- 9 x^{2} + 180 x - 900 = - 4

Move the expression to the left side

- 9 x^{2} + 180 x - 896 = 0

Factor the expression

More Steps

Evaluate

- 9 x^{2} + 180 x - 896

Rewrite the expression

- 9 x^{2} + (84 + 96) x - 896

Calculate

- 9 x^{2} + 84 x + 96 x - 896

Rewrite the expression

- 3 x \times 3 x + 3 x \times 28 + 32 \times 3 x - 32 \times 28

Factor out - 3 x from the expression

- 3 x (3 x - 28) + 32 \times 3 x - 32 \times 28

Factor out 32 from the expression

- 3 x (3 x - 28) + 32 (3 x - 28)

Factor out 3 x - 28 from the expression

(- 3 x + 32) (3 x - 28)

(- 3 x + 32) (3 x - 28) = 0

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

- 3 x + 32 = 0 3 x - 28 = 0

Solve the equation for x

More Steps

Evaluate

- 3 x + 32 = 0

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

- 3 x = 0 - 32

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

- 3 x = - 32

Change the signs on both sides of the equation

3 x = 32

Divide both sides

\frac{3 x}{3} = \frac{32}{3}

Divide the numbers

x = \frac{32}{3}

x = \frac{32}{3} 3 x - 28 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 28 = 0

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

3 x = 0 + 28

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

3 x = 28

Divide both sides

\frac{3 x}{3} = \frac{28}{3}

Divide the numbers

x = \frac{28}{3}

x = \frac{32}{3} x = \frac{28}{3}

Solution

x_{1} = \frac{28}{3}, x_{2} = \frac{32}{3}

Alternative Form

x_{1} = 9. \dot{3}, x_{2} = 10. \dot{6}

Show Solution

Solve the quadratic equation

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