3x^2-11x=101

Simple and best practice solution for 3x^2-11x=101 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 3x^2-11x=101 equation:


Simplifying
3x2 + -11x = 101

Reorder the terms:
-11x + 3x2 = 101

Solving
-11x + 3x2 = 101

Solving for variable 'x'.

Reorder the terms:
-101 + -11x + 3x2 = 101 + -101

Combine like terms: 101 + -101 = 0
-101 + -11x + 3x2 = 0

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

Divide each side by '3'.
-33.66666667 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '33.66666667' to each side of the equation.
-33.66666667 + -3.666666667x + 33.66666667 + x2 = 0 + 33.66666667

Reorder the terms:
-33.66666667 + 33.66666667 + -3.666666667x + x2 = 0 + 33.66666667

Combine like terms: -33.66666667 + 33.66666667 = 0.00000000
0.00000000 + -3.666666667x + x2 = 0 + 33.66666667
-3.666666667x + x2 = 0 + 33.66666667

Combine like terms: 0 + 33.66666667 = 33.66666667
-3.666666667x + x2 = 33.66666667

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 33.66666667 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 33.66666667 + 3.361111114

Combine like terms: 33.66666667 + 3.361111114 = 37.027777784
3.361111114 + -3.666666667x + x2 = 37.027777784

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 37.027777784

Calculate the square root of the right side: 6.085045422

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 6.085045422 and -6.085045422.

Subproblem 1

x + -1.833333334 = 6.085045422 Simplifying x + -1.833333334 = 6.085045422 Reorder the terms: -1.833333334 + x = 6.085045422 Solving -1.833333334 + x = 6.085045422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = 6.085045422 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = 6.085045422 + 1.833333334 x = 6.085045422 + 1.833333334 Combine like terms: 6.085045422 + 1.833333334 = 7.918378756 x = 7.918378756 Simplifying x = 7.918378756

Subproblem 2

x + -1.833333334 = -6.085045422 Simplifying x + -1.833333334 = -6.085045422 Reorder the terms: -1.833333334 + x = -6.085045422 Solving -1.833333334 + x = -6.085045422 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + x = -6.085045422 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + x = -6.085045422 + 1.833333334 x = -6.085045422 + 1.833333334 Combine like terms: -6.085045422 + 1.833333334 = -4.251712088 x = -4.251712088 Simplifying x = -4.251712088

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.918378756, -4.251712088}

See similar equations:

| xlogy+8xy=24 | | 3(x-3.6)=7.2 | | 5x+7y=700 | | 9r+8s-6(5r-2s)= | | xlny+8xy=24 | | 4[6-(1+2x)]+10x=2(10-3x)+8 | | 25x-5=125 | | 7v/5=28 | | 2.5x+4=5x-2 | | ln(x)+ln(2x)= | | 3/26-9/13= | | 3y=6/7 | | 3(x-3.6)=72 | | 6y-3y+=5y-4 | | 78=5v+3 | | 8=4/3y | | y^2-8y=48 | | 128=8(1+3n) | | 3[8x-6]=3 | | (x-7)+(3x+10)=31 | | 4k-6=22k-16-2 | | 8h+11=75 | | (y+8)-y=2 | | 5[3+4k]=115 | | 12=24-6x | | 20uy-8u+35y-14=0 | | 6x+3+x= | | 4y+2=5x+1 | | 2e-f= | | S^2+55=11 | | 3[8]+8=80 | | 14-17/3 |

Equations solver categories