Solve for x 25 = square root of x^2+(24)^2

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Trigonometry

$25 = \sqrt{x^{2} + {(24)}^{2}}$

Rewrite the equation as $\sqrt{x^{2} + {(24)}^{2}} = 25$ .

$\sqrt{x^{2} + {(24)}^{2}} = 25$

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x^{2} + {(24)}^{2}}}^{2} = 25^{2}$

Simplify each side of the equation.

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Multiply the exponents in ${({(x^{2} + {(24)}^{2})}^{\frac{1}{2}})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{2} + {(24)}^{2})}^{\frac{1}{2} \cdot 2} = 25^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

${(x^{2} + {(24)}^{2})}^{\frac{1}{2} \cdot 2} = 25^{2}$

Rewrite the expression.

${(x^{2} + {(24)}^{2})}^{1} = 25^{2}$

Raise $24$ to the power of $2$ .

${(x^{2} + 576)}^{1} = 25^{2}$

Simplify.

$x^{2} + 576 = 25^{2}$

Raise $25$ to the power of $2$ .

$x^{2} + 576 = 625$

Solve for $x$ .

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Move all terms not containing $x$ to the right side of the equation.

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Subtract $576$ from both sides of the equation.

$x^{2} = 625 - 576$

Subtract $576$ from $625$ .

$x^{2} = 49$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{49}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 7$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$x = 7$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 7$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 7, - 7$

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Name

Name	eight hundred sixty-five million nine hundred sixty-one thousand six hundred twenty-seven

Interesting facts

865961627 has 4 divisors, whose sum is 871773600
The reverse of 865961627 is 726169568
Previous prime number is 149

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 50
Digital Root 5

Name

Name	seven hundred fifty-two million one hundred five thousand four hundred forty-eight

Interesting facts

752105448 has 64 divisors, whose sum is 4512633120
The reverse of 752105448 is 844501257
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	eight hundred eight million six hundred sixty-three thousand one hundred forty-two

Interesting facts

808663142 has 16 divisors, whose sum is 1459242240
The reverse of 808663142 is 241366808
Previous prime number is 19

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 38
Digital Root 2

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