3x^2+5x=60

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Solution for 3x^2+5x=60 equation:


Simplifying
3x2 + 5x = 60

Reorder the terms:
5x + 3x2 = 60

Solving
5x + 3x2 = 60

Solving for variable 'x'.

Reorder the terms:
-60 + 5x + 3x2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 5x + 3x2 = 0

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

Divide each side by '3'.
-20 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 1.666666667x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 1.666666667x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 1.666666667x + x2 = 0 + 20
1.666666667x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
1.666666667x + x2 = 20

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 20 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 20 + 0.6944444447

Combine like terms: 20 + 0.6944444447 = 20.6944444447
0.6944444447 + 1.666666667x + x2 = 20.6944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 20.6944444447

Calculate the square root of the right side: 4.549114688

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 4.549114688 and -4.549114688.

Subproblem 1

x + 0.8333333335 = 4.549114688 Simplifying x + 0.8333333335 = 4.549114688 Reorder the terms: 0.8333333335 + x = 4.549114688 Solving 0.8333333335 + x = 4.549114688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 4.549114688 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 4.549114688 + -0.8333333335 x = 4.549114688 + -0.8333333335 Combine like terms: 4.549114688 + -0.8333333335 = 3.7157813545 x = 3.7157813545 Simplifying x = 3.7157813545

Subproblem 2

x + 0.8333333335 = -4.549114688 Simplifying x + 0.8333333335 = -4.549114688 Reorder the terms: 0.8333333335 + x = -4.549114688 Solving 0.8333333335 + x = -4.549114688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -4.549114688 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -4.549114688 + -0.8333333335 x = -4.549114688 + -0.8333333335 Combine like terms: -4.549114688 + -0.8333333335 = -5.3824480215 x = -5.3824480215 Simplifying x = -5.3824480215

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.7157813545, -5.3824480215}

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