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.

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 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 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 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 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