x^2+4*x=45.24

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Solution for x^2+4*x=45.24 equation:


Simplifying
x2 + 4x = 45.24

Reorder the terms:
4x + x2 = 45.24

Solving
4x + x2 = 45.24

Solving for variable 'x'.

Reorder the terms:
-45.24 + 4x + x2 = 45.24 + -45.24

Combine like terms: 45.24 + -45.24 = 0.00
-45.24 + 4x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '45.24' to each side of the equation.
-45.24 + 4x + 45.24 + x2 = 0.00 + 45.24

Reorder the terms:
-45.24 + 45.24 + 4x + x2 = 0.00 + 45.24

Combine like terms: -45.24 + 45.24 = 0.00
0.00 + 4x + x2 = 0.00 + 45.24
4x + x2 = 0.00 + 45.24

Combine like terms: 0.00 + 45.24 = 45.24
4x + x2 = 45.24

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 45.24 + 4

Reorder the terms:
4 + 4x + x2 = 45.24 + 4

Combine like terms: 45.24 + 4 = 49.24
4 + 4x + x2 = 49.24

Factor a perfect square on the left side:
(x + 2)(x + 2) = 49.24

Calculate the square root of the right side: 7.017121917

Break this problem into two subproblems by setting 
(x + 2) equal to 7.017121917 and -7.017121917.

Subproblem 1

x + 2 = 7.017121917 Simplifying x + 2 = 7.017121917 Reorder the terms: 2 + x = 7.017121917 Solving 2 + x = 7.017121917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 7.017121917 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.017121917 + -2 x = 7.017121917 + -2 Combine like terms: 7.017121917 + -2 = 5.017121917 x = 5.017121917 Simplifying x = 5.017121917

Subproblem 2

x + 2 = -7.017121917 Simplifying x + 2 = -7.017121917 Reorder the terms: 2 + x = -7.017121917 Solving 2 + x = -7.017121917 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -7.017121917 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.017121917 + -2 x = -7.017121917 + -2 Combine like terms: -7.017121917 + -2 = -9.017121917 x = -9.017121917 Simplifying x = -9.017121917

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.017121917, -9.017121917}

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