Solve Using the Square Root Property 0=x^2-5x-52

Math
0=x2-5x-52
Rewrite the equation as x2-5x-52=0.
x2-5x-52=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-5, and c=-52 into the quadratic formula and solve for x.
5±(-5)2-4⋅(1⋅-52)2⋅1
Simplify.
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Simplify the numerator.
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Raise -5 to the power of 2.
x=5±25-4⋅(1⋅-52)2⋅1
Multiply -52 by 1.
x=5±25-4⋅-522⋅1
Multiply -4 by -52.
x=5±25+2082⋅1
Add 25 and 208.
x=5±2332⋅1
x=5±2332⋅1
Multiply 2 by 1.
x=5±2332
x=5±2332
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -5 to the power of 2.
x=5±25-4⋅(1⋅-52)2⋅1
Multiply -52 by 1.
x=5±25-4⋅-522⋅1
Multiply -4 by -52.
x=5±25+2082⋅1
Add 25 and 208.
x=5±2332⋅1
x=5±2332⋅1
Multiply 2 by 1.
x=5±2332
Change the ± to +.
x=5+2332
x=5+2332
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -5 to the power of 2.
x=5±25-4⋅(1⋅-52)2⋅1
Multiply -52 by 1.
x=5±25-4⋅-522⋅1
Multiply -4 by -52.
x=5±25+2082⋅1
Add 25 and 208.
x=5±2332⋅1
x=5±2332⋅1
Multiply 2 by 1.
x=5±2332
Change the ± to -.
x=5-2332
x=5-2332
The final answer is the combination of both solutions.
x=5+2332,5-2332
The result can be shown in multiple forms.
Exact Form:
x=5+2332,5-2332
Decimal Form:
x=10.13216876…,-5.13216876…
Solve Using the Square Root Property 0=x^2-5x-52

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