# Solve using the Square Root Property 4x^2-12x+9=5

4×2-12x+9=5
Move 5 to the left side of the equation by subtracting it from both sides.
4×2-12x+9-5=0
Subtract 5 from 9.
4×2-12x+4=0
Factor 4 out of 4×2-12x+4.
Factor 4 out of 4×2.
4(x2)-12x+4=0
Factor 4 out of -12x.
4(x2)+4(-3x)+4=0
Factor 4 out of 4.
4(x2)+4(-3x)+4(1)=0
Factor 4 out of 4(x2)+4(-3x).
4(x2-3x)+4(1)=0
Factor 4 out of 4(x2-3x)+4(1).
4(x2-3x+1)=0
4(x2-3x+1)=0
Divide each term by 4 and simplify.
Divide each term in 4(x2-3x+1)=0 by 4.
4(x2-3x+1)4=04
Cancel the common factor of 4.
Cancel the common factor.
4(x2-3x+1)4=04
Divide x2-3x+1 by 1.
x2-3x+1=04
x2-3x+1=04
Divide 0 by 4.
x2-3x+1=0
x2-3x+1=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-3, and c=1 into the quadratic formula and solve for x.
3±(-3)2-4⋅(1⋅1)2⋅1
Simplify.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅1)2⋅1
Multiply 1 by 1.
x=3±9-4⋅12⋅1
Multiply -4 by 1.
x=3±9-42⋅1
Subtract 4 from 9.
x=3±52⋅1
x=3±52⋅1
Multiply 2 by 1.
x=3±52
x=3±52
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅1)2⋅1
Multiply 1 by 1.
x=3±9-4⋅12⋅1
Multiply -4 by 1.
x=3±9-42⋅1
Subtract 4 from 9.
x=3±52⋅1
x=3±52⋅1
Multiply 2 by 1.
x=3±52
Change the ± to +.
x=3+52
x=3+52
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -3 to the power of 2.
x=3±9-4⋅(1⋅1)2⋅1
Multiply 1 by 1.
x=3±9-4⋅12⋅1
Multiply -4 by 1.
x=3±9-42⋅1
Subtract 4 from 9.
x=3±52⋅1
x=3±52⋅1
Multiply 2 by 1.
x=3±52
Change the ± to -.
x=3-52
x=3-52
The final answer is the combination of both solutions.
x=3+52,3-52
The result can be shown in multiple forms.
Exact Form:
x=3+52,3-52
Decimal Form:
x=2.61803398…,0.38196601…
Solve using the Square Root Property 4x^2-12x+9=5