Solve 27x^2-147 - ScanMath

Question

Factor the expression

3 (3 x - 7) (3 x + 7)

Evaluate

27 x^{2} - 147

Factor out 3 from the expression

3 (9 x^{2} - 49)

Solution

More Steps

Evaluate

9 x^{2} - 49

Rewrite the expression in exponential form

(3 x)^{2} - 7^{2}

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

(3 x - 7) (3 x + 7)

3 (3 x - 7) (3 x + 7)

Show Solution

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

Alternative Form

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

Evaluate

27 x^{2} - 147

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

27 x^{2} - 147 = 0

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

27 x^{2} = 0 + 147

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

27 x^{2} = 147

Divide both sides

\frac{27 x ^{2}}{27} = \frac{147}{27}

Divide the numbers

x^{2} = \frac{147}{27}

Cancel out the common factor 3

x^{2} = \frac{49}{9}

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

x = \pm \frac{49}{9}

Simplify the expression

More Steps

Evaluate

\frac{49}{9}

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

\frac{49}{9}

Simplify the radical expression

More Steps

Evaluate

49

Write the number in exponential form with the base of 7

7^{2}

Reduce the index of the radical and exponent with 2

7

\frac{7}{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{7}{3}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution