2025=x^2+14x+45

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Solution for 2025=x^2+14x+45 equation:


Simplifying
2025 = x2 + 14x + 45

Reorder the terms:
2025 = 45 + 14x + x2

Solving
2025 = 45 + 14x + x2

Solving for variable 'x'.

Combine like terms: 2025 + -45 = 1980
1980 + -14x + -1x2 = 45 + 14x + x2 + -45 + -14x + -1x2

Reorder the terms:
1980 + -14x + -1x2 = 45 + -45 + 14x + -14x + x2 + -1x2

Combine like terms: 45 + -45 = 0
1980 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
1980 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
1980 + -14x + -1x2 = 0 + x2 + -1x2
1980 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1980 + -14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1980 + 14x + x2 = 0

Move the constant term to the right:

Add '1980' to each side of the equation.
-1980 + 14x + 1980 + x2 = 0 + 1980

Reorder the terms:
-1980 + 1980 + 14x + x2 = 0 + 1980

Combine like terms: -1980 + 1980 = 0
0 + 14x + x2 = 0 + 1980
14x + x2 = 0 + 1980

Combine like terms: 0 + 1980 = 1980
14x + x2 = 1980

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 1980 + 49

Reorder the terms:
49 + 14x + x2 = 1980 + 49

Combine like terms: 1980 + 49 = 2029
49 + 14x + x2 = 2029

Factor a perfect square on the left side:
(x + 7)(x + 7) = 2029

Calculate the square root of the right side: 45.044422518

Break this problem into two subproblems by setting 
(x + 7) equal to 45.044422518 and -45.044422518.

Subproblem 1

x + 7 = 45.044422518 Simplifying x + 7 = 45.044422518 Reorder the terms: 7 + x = 45.044422518 Solving 7 + x = 45.044422518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 45.044422518 + -7 Combine like terms: 7 + -7 = 0 0 + x = 45.044422518 + -7 x = 45.044422518 + -7 Combine like terms: 45.044422518 + -7 = 38.044422518 x = 38.044422518 Simplifying x = 38.044422518

Subproblem 2

x + 7 = -45.044422518 Simplifying x + 7 = -45.044422518 Reorder the terms: 7 + x = -45.044422518 Solving 7 + x = -45.044422518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -45.044422518 + -7 Combine like terms: 7 + -7 = 0 0 + x = -45.044422518 + -7 x = -45.044422518 + -7 Combine like terms: -45.044422518 + -7 = -52.044422518 x = -52.044422518 Simplifying x = -52.044422518

Solution

The solution to the problem is based on the solutions from the subproblems. x = {38.044422518, -52.044422518}

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