Solve Using the Square Root Property 10=-5x^2+23x+23

Math
10=-5×2+23x+23
Rewrite the equation as -5×2+23x+23=10.
-5×2+23x+23=10
Move 10 to the left side of the equation by subtracting it from both sides.
-5×2+23x+23-10=0
Subtract 10 from 23.
-5×2+23x+13=0
Factor -1 out of -5×2+23x+13.
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Factor -1 out of -5×2.
-(5×2)+23x+13=0
Factor -1 out of 23x.
-(5×2)-(-23x)+13=0
Rewrite 13 as -1(-13).
-(5×2)-(-23x)-1⋅-13=0
Factor -1 out of -(5×2)-(-23x).
-(5×2-23x)-1⋅-13=0
Factor -1 out of -(5×2-23x)-1(-13).
-(5×2-23x-13)=0
-(5×2-23x-13)=0
Multiply each term in -(5×2-23x-13)=0 by -1
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Multiply each term in -(5×2-23x-13)=0 by -1.
-(5×2-23x-13)⋅-1=0⋅-1
Simplify -(5×2-23x-13)⋅-1.
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Apply the distributive property.
(-(5×2)-(-23x)–13)⋅-1=0⋅-1
Simplify.
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Multiply 5 by -1.
(-5×2-(-23x)–13)⋅-1=0⋅-1
Multiply -23 by -1.
(-5×2+23x–13)⋅-1=0⋅-1
Multiply -1 by -13.
(-5×2+23x+13)⋅-1=0⋅-1
(-5×2+23x+13)⋅-1=0⋅-1
Apply the distributive property.
-5×2⋅-1+23x⋅-1+13⋅-1=0⋅-1
Simplify.
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Multiply -1 by -5.
5×2+23x⋅-1+13⋅-1=0⋅-1
Multiply -1 by 23.
5×2-23x+13⋅-1=0⋅-1
Multiply 13 by -1.
5×2-23x-13=0⋅-1
5×2-23x-13=0⋅-1
5×2-23x-13=0⋅-1
Multiply 0 by -1.
5×2-23x-13=0
5×2-23x-13=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=5, b=-23, and c=-13 into the quadratic formula and solve for x.
23±(-23)2-4⋅(5⋅-13)2⋅5
Simplify.
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Simplify the numerator.
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Raise -23 to the power of 2.
x=23±529-4⋅(5⋅-13)2⋅5
Multiply 5 by -13.
x=23±529-4⋅-652⋅5
Multiply -4 by -65.
x=23±529+2602⋅5
Add 529 and 260.
x=23±7892⋅5
x=23±7892⋅5
Multiply 2 by 5.
x=23±78910
x=23±78910
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -23 to the power of 2.
x=23±529-4⋅(5⋅-13)2⋅5
Multiply 5 by -13.
x=23±529-4⋅-652⋅5
Multiply -4 by -65.
x=23±529+2602⋅5
Add 529 and 260.
x=23±7892⋅5
x=23±7892⋅5
Multiply 2 by 5.
x=23±78910
Change the ± to +.
x=23+78910
x=23+78910
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -23 to the power of 2.
x=23±529-4⋅(5⋅-13)2⋅5
Multiply 5 by -13.
x=23±529-4⋅-652⋅5
Multiply -4 by -65.
x=23±529+2602⋅5
Add 529 and 260.
x=23±7892⋅5
x=23±7892⋅5
Multiply 2 by 5.
x=23±78910
Change the ± to -.
x=23-78910
x=23-78910
The final answer is the combination of both solutions.
x=23+78910,23-78910
The result can be shown in multiple forms.
Exact Form:
x=23+78910,23-78910
Decimal Form:
x=5.10891438…,-0.50891438…
Solve Using the Square Root Property 10=-5x^2+23x+23

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