Solve (3-2x)(3+2x)

Question

Simplify the expression

9 - 4 x^{2}

Evaluate

(3 - 2 x) (3 + 2 x)

Use (a - b) (a + b) = a^{2} - b^{2} to simplify the product

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

Evaluate the power

9 - (2 x)^{2}

Solution

More Steps

Evaluate

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

9 - 4 x^{2}

Show Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 1.5

Evaluate

(3 - 2 x) (3 + 2 x)

To find the roots of the expression,set the expression equal to 0

(3 - 2 x) (3 + 2 x) = 0

Separate the equation into 2 possible cases

3 - 2 x = 0 3 + 2 x = 0

Solve the equation

More Steps

Evaluate

3 - 2 x = 0

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

- 2 x = 0 - 3

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

- 2 x = - 3

Change the signs on both sides of the equation

2 x = 3

Divide both sides

\frac{2 x}{2} = \frac{3}{2}

Divide the numbers

x = \frac{3}{2}

x = \frac{3}{2} 3 + 2 x = 0

Solve the equation

More Steps

Evaluate

3 + 2 x = 0

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

2 x = 0 - 3

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

2 x = - 3

Divide both sides

\frac{2 x}{2} = \frac{- 3}{2}

Divide the numbers

x = \frac{- 3}{2}

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

x = - \frac{3}{2}

x = \frac{3}{2} x = - \frac{3}{2}

Solution

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

Alternative Form

x_{1} = - 1.5, x_{2} = 1.5

Show Solution