x^2+3x=42

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Solution for x^2+3x=42 equation:


Simplifying
x2 + 3x = 42

Reorder the terms:
3x + x2 = 42

Solving
3x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + 3x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 3x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 3x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 3x + x2 = 0 + 42
3x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
3x + x2 = 42

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 = 42 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 42 + 2.25

Combine like terms: 42 + 2.25 = 44.25
2.25 + 3x + x2 = 44.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

x + 1.5 = 6.652067348 Simplifying x + 1.5 = 6.652067348 Reorder the terms: 1.5 + x = 6.652067348 Solving 1.5 + x = 6.652067348 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 = 6.652067348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.652067348 + -1.5 x = 6.652067348 + -1.5 Combine like terms: 6.652067348 + -1.5 = 5.152067348 x = 5.152067348 Simplifying x = 5.152067348

Subproblem 2

x + 1.5 = -6.652067348 Simplifying x + 1.5 = -6.652067348 Reorder the terms: 1.5 + x = -6.652067348 Solving 1.5 + x = -6.652067348 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 = -6.652067348 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.652067348 + -1.5 x = -6.652067348 + -1.5 Combine like terms: -6.652067348 + -1.5 = -8.152067348 x = -8.152067348 Simplifying x = -8.152067348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.152067348, -8.152067348}

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