4x^2-6x=21

Simple and best practice solution for 4x^2-6x=21 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^2-6x=21 equation:


Simplifying
4x2 + -6x = 21

Reorder the terms:
-6x + 4x2 = 21

Solving
-6x + 4x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -6x + 4x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -6x + 4x2 = 0

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

Divide each side by '4'.
-5.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -1.5x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -1.5x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -1.5x + x2 = 0 + 5.25
-1.5x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-1.5x + x2 = 5.25

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 = 5.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 5.25 + 0.5625

Combine like terms: 5.25 + 0.5625 = 5.8125
0.5625 + -1.5x + x2 = 5.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 5.8125

Calculate the square root of the right side: 2.41091269

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.41091269 and -2.41091269.

Subproblem 1

x + -0.75 = 2.41091269 Simplifying x + -0.75 = 2.41091269 Reorder the terms: -0.75 + x = 2.41091269 Solving -0.75 + x = 2.41091269 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 = 2.41091269 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.41091269 + 0.75 x = 2.41091269 + 0.75 Combine like terms: 2.41091269 + 0.75 = 3.16091269 x = 3.16091269 Simplifying x = 3.16091269

Subproblem 2

x + -0.75 = -2.41091269 Simplifying x + -0.75 = -2.41091269 Reorder the terms: -0.75 + x = -2.41091269 Solving -0.75 + x = -2.41091269 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 = -2.41091269 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.41091269 + 0.75 x = -2.41091269 + 0.75 Combine like terms: -2.41091269 + 0.75 = -1.66091269 x = -1.66091269 Simplifying x = -1.66091269

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.16091269, -1.66091269}

See similar equations:

| 8(-4r+4)+6=-16-5r | | 6d-1=6+7d | | -7(7)+y=5 | | 20=4-4x | | -7(4)+y=5 | | 2x^2-12=2x | | 2x^2-12=2x | | -7(-1)+y=5 | | -355=13a-4 | | 4y-10x=0 | | 6=1+5x | | 8-2x+7-4x=3(x-4) | | 8(-4t+4)+6=-16-5r | | 23=7(8-d) | | m+.20m=54 | | 2(6m+3)=15+3m | | 4(1-5x)=-136 | | 18-5p=p | | 4(1-5)=-136 | | 495x=10+12x | | 4=7x+10 | | 15-.1x=.15x | | 2w-9=3w+10 | | -4+4x+5x+12=91 | | 4+7x+4=15 | | -2x-3+4=5+1x | | 7(x-6)+19=4(x-5) | | 1-3r=-14-6r | | u^2-2u-8=0 | | (3x)(3x)+2x-16=0 | | 0.25(c)=60 | | 1x-5=-1x+3 |

Equations solver categories