x^2+3x-40=20

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Solution for x^2+3x-40=20 equation:


Simplifying
x2 + 3x + -40 = 20

Reorder the terms:
-40 + 3x + x2 = 20

Solving
-40 + 3x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-40 + -20 + 3x + x2 = 20 + -20

Combine like terms: -40 + -20 = -60
-60 + 3x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-60 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 3x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + 3x + x2 = 0 + 60

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

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

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 60 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 60 + 2.25

Combine like terms: 60 + 2.25 = 62.25
2.25 + 3x + x2 = 62.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

x + 1.5 = 7.889866919 Simplifying x + 1.5 = 7.889866919 Reorder the terms: 1.5 + x = 7.889866919 Solving 1.5 + x = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.889866919 + -1.5 x = 7.889866919 + -1.5 Combine like terms: 7.889866919 + -1.5 = 6.389866919 x = 6.389866919 Simplifying x = 6.389866919

Subproblem 2

x + 1.5 = -7.889866919 Simplifying x + 1.5 = -7.889866919 Reorder the terms: 1.5 + x = -7.889866919 Solving 1.5 + x = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.889866919 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.889866919 + -1.5 x = -7.889866919 + -1.5 Combine like terms: -7.889866919 + -1.5 = -9.389866919 x = -9.389866919 Simplifying x = -9.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.389866919, -9.389866919}

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