# Solve Using the Square Root Property 0=x^2-10x+3000 0=x2-10x+3000
Rewrite the equation as x2-10x+3000=0.
x2-10x+3000=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-10, and c=3000 into the quadratic formula and solve for x.
10±(-10)2-4⋅(1⋅3000)2⋅1
Simplify.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅3000)2⋅1
Multiply 3000 by 1.
x=10±100-4⋅30002⋅1
Multiply -4 by 3000.
x=10±100-120002⋅1
Subtract 12000 from 100.
x=10±-119002⋅1
Rewrite -11900 as -1(11900).
x=10±-1⋅119002⋅1
Rewrite -1(11900) as -1⋅11900.
x=10±-1⋅119002⋅1
Rewrite -1 as i.
x=10±i⋅119002⋅1
Rewrite 11900 as 102⋅119.
Factor 100 out of 11900.
x=10±i⋅100(119)2⋅1
Rewrite 100 as 102.
x=10±i⋅102⋅1192⋅1
x=10±i⋅102⋅1192⋅1
Pull terms out from under the radical.
x=10±i⋅(10119)2⋅1
Move 10 to the left of i.
x=10±10i1192⋅1
x=10±10i1192⋅1
Multiply 2 by 1.
x=10±10i1192
Simplify 10±10i1192.
x=5±5i119
x=5±5i119
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅3000)2⋅1
Multiply 3000 by 1.
x=10±100-4⋅30002⋅1
Multiply -4 by 3000.
x=10±100-120002⋅1
Subtract 12000 from 100.
x=10±-119002⋅1
Rewrite -11900 as -1(11900).
x=10±-1⋅119002⋅1
Rewrite -1(11900) as -1⋅11900.
x=10±-1⋅119002⋅1
Rewrite -1 as i.
x=10±i⋅119002⋅1
Rewrite 11900 as 102⋅119.
Factor 100 out of 11900.
x=10±i⋅100(119)2⋅1
Rewrite 100 as 102.
x=10±i⋅102⋅1192⋅1
x=10±i⋅102⋅1192⋅1
Pull terms out from under the radical.
x=10±i⋅(10119)2⋅1
Move 10 to the left of i.
x=10±10i1192⋅1
x=10±10i1192⋅1
Multiply 2 by 1.
x=10±10i1192
Simplify 10±10i1192.
x=5±5i119
Change the ± to +.
x=5+5i119
x=5+5i119
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -10 to the power of 2.
x=10±100-4⋅(1⋅3000)2⋅1
Multiply 3000 by 1.
x=10±100-4⋅30002⋅1
Multiply -4 by 3000.
x=10±100-120002⋅1
Subtract 12000 from 100.
x=10±-119002⋅1
Rewrite -11900 as -1(11900).
x=10±-1⋅119002⋅1
Rewrite -1(11900) as -1⋅11900.
x=10±-1⋅119002⋅1
Rewrite -1 as i.
x=10±i⋅119002⋅1
Rewrite 11900 as 102⋅119.
Factor 100 out of 11900.
x=10±i⋅100(119)2⋅1
Rewrite 100 as 102.
x=10±i⋅102⋅1192⋅1
x=10±i⋅102⋅1192⋅1
Pull terms out from under the radical.
x=10±i⋅(10119)2⋅1
Move 10 to the left of i.
x=10±10i1192⋅1
x=10±10i1192⋅1
Multiply 2 by 1.
x=10±10i1192
Simplify 10±10i1192.
x=5±5i119
Change the ± to -.
x=5-5i119
x=5-5i119
The final answer is the combination of both solutions.
x=5+5i119,5-5i119
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