Solve ( - 3 x - 5 ) ( x ^ { 2 } - 9 ) = 0

Question

Solve the equation

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

Alternative Form

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

Evaluate

(- 3 x - 5) (x^{2} - 9) = 0

Change the sign

(3 x + 5) (x^{2} - 9) = 0

Separate the equation into 2 possible cases

3 x + 5 = 0 x^{2} - 9 = 0

Solve the equation

More Steps

Evaluate

3 x + 5 = 0

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

3 x = 0 - 5

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

3 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{3}

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

x = - \frac{5}{3}

x = - \frac{5}{3} x^{2} - 9 = 0

Solve the equation

More Steps

Evaluate

x^{2} - 9 = 0

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

x^{2} = 0 + 9

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

x^{2} = 9

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 9

Simplify the expression

More Steps

Evaluate

9

Write the number in exponential form with the base of 3

3^{2}

Reduce the index of the radical and exponent with 2

3

x = \pm 3

Separate the equation into 2 possible cases

x = 3 x = - 3

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

Solution

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

Alternative Form

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

Show Solution

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