Solve 15^2-(6 x)^2

Question

Simplify the expression

225 - 36 x^{2}

Evaluate

1 5^{2} - (6 x)^{2}

Evaluate the power

225 - (6 x)^{2}

Solution

225 - 36 x^{2}

Show Solution

Factor the expression

9 (5 - 2 x) (5 + 2 x)

Evaluate

1 5^{2} - (6 x)^{2}

Evaluate

225 - (6 x)^{2}

Evaluate

More Steps

Evaluate

(6 x)^{2}

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

6^{2} x^{2}

Evaluate the power

36 x^{2}

225 - 36 x^{2}

Factor out 9 from the expression

9 (25 - 4 x^{2})

Solution

More Steps

Evaluate

25 - 4 x^{2}

Rewrite the expression in exponential form

5^{2} - (2 x)^{2}

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

(5 - 2 x) (5 + 2 x)

9 (5 - 2 x) (5 + 2 x)

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 2.5, x_{2} = 2.5

Evaluate

1 5^{2} - (6 x)^{2}

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

1 5^{2} - (6 x)^{2} = 0

Subtract the terms

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Simplify

1 5^{2} - (6 x)^{2}

Evaluate the power

225 - (6 x)^{2}

Rewrite the expression

More Steps

Evaluate

(6 x)^{2}

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

6^{2} x^{2}

Evaluate the power

36 x^{2}

225 - 36 x^{2}

225 - 36 x^{2} = 0

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

- 36 x^{2} = 0 - 225

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

- 36 x^{2} = - 225

Change the signs on both sides of the equation

36 x^{2} = 225

Divide both sides

\frac{36 x ^{2}}{36} = \frac{225}{36}

Divide the numbers

x^{2} = \frac{225}{36}

Cancel out the common factor 9

x^{2} = \frac{25}{4}

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

x = \pm \frac{25}{4}

Simplify the expression

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Evaluate

\frac{25}{4}

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

\frac{25}{4}

Simplify the radical expression

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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}{4}

Simplify the radical expression

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Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{5}{2}

x = \pm \frac{5}{2}

Separate the equation into 2 possible cases

x = \frac{5}{2} x = - \frac{5}{2}

Solution

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

Alternative Form

x_{1} = - 2.5, x_{2} = 2.5

Show Solution