Solve 49x^(2)-144 - Socratic AI (ScanMath)

Question

Factor the expression

(7 x - 12) (7 x + 12)

Evaluate

49 x^{2} - 144

Rewrite the expression in exponential form

(7 x)^{2} - 1 2^{2}

Solution

(7 x - 12) (7 x + 12)

Show Solution

x_{1} = - \frac{12}{7}, x_{2} = \frac{12}{7}

Alternative Form

x_{1} = - 1. \dot{7} 1428 \dot{5}, x_{2} = 1. \dot{7} 1428 \dot{5}

Evaluate

49 x^{2} - 144

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

49 x^{2} - 144 = 0

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

49 x^{2} = 0 + 144

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

49 x^{2} = 144

Divide both sides

\frac{49 x ^{2}}{49} = \frac{144}{49}

Divide the numbers

x^{2} = \frac{144}{49}

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

x = \pm \frac{144}{49}

Simplify the expression

More Steps

Evaluate

\frac{144}{49}

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

\frac{144}{49}

Simplify the radical expression

More Steps

Evaluate

144

Write the number in exponential form with the base of 12

1 2^{2}

Reduce the index of the radical and exponent with 2

12

\frac{12}{49}

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{12}{7}

x = \pm \frac{12}{7}

Separate the equation into 2 possible cases

x = \frac{12}{7} x = - \frac{12}{7}

Solution

x_{1} = - \frac{12}{7}, x_{2} = \frac{12}{7}

Alternative Form

x_{1} = - 1. \dot{7} 1428 \dot{5}, x_{2} = 1. \dot{7} 1428 \dot{5}

Show Solution