Solve Using the Square Root Property x^2=6x-10

Math
x2=6x-10
Subtract 6x from both sides of the equation.
x2-6x=-10
Move 10 to the left side of the equation by adding it to both sides.
x2-6x+10=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-6, and c=10 into the quadratic formula and solve for x.
6±(-6)2-4⋅(1⋅10)2⋅1
Simplify.
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Simplify the numerator.
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Raise -6 to the power of 2.
x=6±36-4⋅(1⋅10)2⋅1
Multiply 10 by 1.
x=6±36-4⋅102⋅1
Multiply -4 by 10.
x=6±36-402⋅1
Subtract 40 from 36.
x=6±-42⋅1
Rewrite -4 as -1(4).
x=6±-1⋅42⋅1
Rewrite -1(4) as -1⋅4.
x=6±-1⋅42⋅1
Rewrite -1 as i.
x=6±i⋅42⋅1
Rewrite 4 as 22.
x=6±i⋅222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅22⋅1
Move 2 to the left of i.
x=6±2i2⋅1
x=6±2i2⋅1
Multiply 2 by 1.
x=6±2i2
Simplify 6±2i2.
x=3±i
x=3±i
Simplify the expression to solve for the + portion of the ±.
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Simplify the numerator.
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Raise -6 to the power of 2.
x=6±36-4⋅(1⋅10)2⋅1
Multiply 10 by 1.
x=6±36-4⋅102⋅1
Multiply -4 by 10.
x=6±36-402⋅1
Subtract 40 from 36.
x=6±-42⋅1
Rewrite -4 as -1(4).
x=6±-1⋅42⋅1
Rewrite -1(4) as -1⋅4.
x=6±-1⋅42⋅1
Rewrite -1 as i.
x=6±i⋅42⋅1
Rewrite 4 as 22.
x=6±i⋅222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅22⋅1
Move 2 to the left of i.
x=6±2i2⋅1
x=6±2i2⋅1
Multiply 2 by 1.
x=6±2i2
Simplify 6±2i2.
x=3±i
Change the ± to +.
x=3+i
x=3+i
Simplify the expression to solve for the – portion of the ±.
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Simplify the numerator.
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Raise -6 to the power of 2.
x=6±36-4⋅(1⋅10)2⋅1
Multiply 10 by 1.
x=6±36-4⋅102⋅1
Multiply -4 by 10.
x=6±36-402⋅1
Subtract 40 from 36.
x=6±-42⋅1
Rewrite -4 as -1(4).
x=6±-1⋅42⋅1
Rewrite -1(4) as -1⋅4.
x=6±-1⋅42⋅1
Rewrite -1 as i.
x=6±i⋅42⋅1
Rewrite 4 as 22.
x=6±i⋅222⋅1
Pull terms out from under the radical, assuming positive real numbers.
x=6±i⋅22⋅1
Move 2 to the left of i.
x=6±2i2⋅1
x=6±2i2⋅1
Multiply 2 by 1.
x=6±2i2
Simplify 6±2i2.
x=3±i
Change the ± to -.
x=3-i
x=3-i
The final answer is the combination of both solutions.
x=3+i,3-i
Solve Using the Square Root Property x^2=6x-10

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