4x^2+1=6x

Simple and best practice solution for 4x^2+1=6x equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4x^2+1=6x equation:


Simplifying
4x2 + 1 = 6x

Reorder the terms:
1 + 4x2 = 6x

Solving
1 + 4x2 = 6x

Solving for variable 'x'.

Reorder the terms:
1 + -6x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
1 + -6x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
0.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -1.5x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -1.5x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -1.5x + x2 = 0 + -0.25
-1.5x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-1.5x + x2 = -0.25

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = -0.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = -0.25 + 0.5625

Combine like terms: -0.25 + 0.5625 = 0.3125
0.5625 + -1.5x + x2 = 0.3125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + -0.75) equal to 0.559016994 and -0.559016994.

Subproblem 1

x + -0.75 = 0.559016994 Simplifying x + -0.75 = 0.559016994 Reorder the terms: -0.75 + x = 0.559016994 Solving -0.75 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.559016994 + 0.75 x = 0.559016994 + 0.75 Combine like terms: 0.559016994 + 0.75 = 1.309016994 x = 1.309016994 Simplifying x = 1.309016994

Subproblem 2

x + -0.75 = -0.559016994 Simplifying x + -0.75 = -0.559016994 Reorder the terms: -0.75 + x = -0.559016994 Solving -0.75 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.559016994 + 0.75 x = -0.559016994 + 0.75 Combine like terms: -0.559016994 + 0.75 = 0.190983006 x = 0.190983006 Simplifying x = 0.190983006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.309016994, 0.190983006}

See similar equations:

| 8x-9=8(x+2) | | 4x+10+3x+5+5x-25=90 | | 2x+8=43-3x | | 6x+8y=226 | | 9(3)+3y=54 | | 8x-10=3x-10 | | 9+11x=99+x | | 9x+3(0)=54 | | 6X-3=2x-6 | | 9(0)+3y=54 | | c^2=8c | | 5x+3x+(2x+5)=180 | | 8m-26=-50+4m | | 8(d-5)+(4d+7)= | | 9x+6-3x=-8+4x | | -1(5a+6)=2(3a+8) | | 8m-2b=-50+4m | | 8x+(2x+5)=90 | | 7x+12= | | 5x-1=13x-57 | | 5x-7(-10)=35 | | 7b-16=-18+9b | | 8z-9=9z-3 | | -4(5n-6)+3n= | | 5x-7(0)=35 | | b+(b-4)=(b+5)-(b+1) | | 5x+3x=(2x+5) | | -7t+3t= | | -2(3x-4)=2x | | 5(0)-7y=35 | | 7.4a=-37 | | 5x+3x+(2x+5)=90 |

Equations solver categories