Solve 18a^2 - 50 - ScanMath

Question

Factor the expression

2 (3 a - 5) (3 a + 5)

Evaluate

18 a^{2} - 50

Factor out 2 from the expression

2 (9 a^{2} - 25)

Solution

More Steps

Evaluate

9 a^{2} - 25

Rewrite the expression in exponential form

(3 a)^{2} - 5^{2}

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

(3 a - 5) (3 a + 5)

2 (3 a - 5) (3 a + 5)

Show Solution

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

Alternative Form

a_{1} = - 1. \dot{6}, a_{2} = 1. \dot{6}

Evaluate

18 a^{2} - 50

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

18 a^{2} - 50 = 0

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

18 a^{2} = 0 + 50

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

18 a^{2} = 50

Divide both sides

\frac{18 a ^{2}}{18} = \frac{50}{18}

Divide the numbers

a^{2} = \frac{50}{18}

Cancel out the common factor 2

a^{2} = \frac{25}{9}

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

a = \pm \frac{25}{9}

Simplify the expression

More Steps

Evaluate

\frac{25}{9}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{25}{9}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{9}

Simplify the radical 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

\frac{5}{3}

a = \pm \frac{5}{3}

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

a_{1} = - 1. \dot{6}, a_{2} = 1. \dot{6}

Show Solution