40=0.25x^2+3x-40

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Solution for 40=0.25x^2+3x-40 equation:


Simplifying
40 = 0.25x2 + 3x + -40

Reorder the terms:
40 = -40 + 3x + 0.25x2

Solving
40 = -40 + 3x + 0.25x2

Solving for variable 'x'.

Combine like terms: 40 + 40 = 80
80 + -3x + -0.25x2 = -40 + 3x + 0.25x2 + 40 + -3x + -0.25x2

Reorder the terms:
80 + -3x + -0.25x2 = -40 + 40 + 3x + -3x + 0.25x2 + -0.25x2

Combine like terms: -40 + 40 = 0
80 + -3x + -0.25x2 = 0 + 3x + -3x + 0.25x2 + -0.25x2
80 + -3x + -0.25x2 = 3x + -3x + 0.25x2 + -0.25x2

Combine like terms: 3x + -3x = 0
80 + -3x + -0.25x2 = 0 + 0.25x2 + -0.25x2
80 + -3x + -0.25x2 = 0.25x2 + -0.25x2

Combine like terms: 0.25x2 + -0.25x2 = 0.00
80 + -3x + -0.25x2 = 0.00

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
-320 + 12x + x2 = 0

Move the constant term to the right:

Add '320' to each side of the equation.
-320 + 12x + 320 + x2 = 0 + 320

Reorder the terms:
-320 + 320 + 12x + x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 12x + x2 = 0 + 320
12x + x2 = 0 + 320

Combine like terms: 0 + 320 = 320
12x + x2 = 320

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 320 + 36

Reorder the terms:
36 + 12x + x2 = 320 + 36

Combine like terms: 320 + 36 = 356
36 + 12x + x2 = 356

Factor a perfect square on the left side:
(x + 6)(x + 6) = 356

Calculate the square root of the right side: 18.867962264

Break this problem into two subproblems by setting 
(x + 6) equal to 18.867962264 and -18.867962264.

Subproblem 1

x + 6 = 18.867962264 Simplifying x + 6 = 18.867962264 Reorder the terms: 6 + x = 18.867962264 Solving 6 + x = 18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 18.867962264 + -6 Combine like terms: 6 + -6 = 0 0 + x = 18.867962264 + -6 x = 18.867962264 + -6 Combine like terms: 18.867962264 + -6 = 12.867962264 x = 12.867962264 Simplifying x = 12.867962264

Subproblem 2

x + 6 = -18.867962264 Simplifying x + 6 = -18.867962264 Reorder the terms: 6 + x = -18.867962264 Solving 6 + x = -18.867962264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -18.867962264 + -6 Combine like terms: 6 + -6 = 0 0 + x = -18.867962264 + -6 x = -18.867962264 + -6 Combine like terms: -18.867962264 + -6 = -24.867962264 x = -24.867962264 Simplifying x = -24.867962264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.867962264, -24.867962264}

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