146=x^2+7x

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Solution for 146=x^2+7x equation:


Simplifying
146 = x2 + 7x

Reorder the terms:
146 = 7x + x2

Solving
146 = 7x + x2

Solving for variable 'x'.

Reorder the terms:
146 + -7x + -1x2 = 7x + -7x + x2 + -1x2

Combine like terms: 7x + -7x = 0
146 + -7x + -1x2 = 0 + x2 + -1x2
146 + -7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
146 + -7x + -1x2 = 0

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

Divide each side by '-1'.
-146 + 7x + x2 = 0

Move the constant term to the right:

Add '146' to each side of the equation.
-146 + 7x + 146 + x2 = 0 + 146

Reorder the terms:
-146 + 146 + 7x + x2 = 0 + 146

Combine like terms: -146 + 146 = 0
0 + 7x + x2 = 0 + 146
7x + x2 = 0 + 146

Combine like terms: 0 + 146 = 146
7x + x2 = 146

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 146 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 146 + 12.25

Combine like terms: 146 + 12.25 = 158.25
12.25 + 7x + x2 = 158.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 158.25

Calculate the square root of the right side: 12.579745625

Break this problem into two subproblems by setting 
(x + 3.5) equal to 12.579745625 and -12.579745625.

Subproblem 1

x + 3.5 = 12.579745625 Simplifying x + 3.5 = 12.579745625 Reorder the terms: 3.5 + x = 12.579745625 Solving 3.5 + x = 12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 12.579745625 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 12.579745625 + -3.5 x = 12.579745625 + -3.5 Combine like terms: 12.579745625 + -3.5 = 9.079745625 x = 9.079745625 Simplifying x = 9.079745625

Subproblem 2

x + 3.5 = -12.579745625 Simplifying x + 3.5 = -12.579745625 Reorder the terms: 3.5 + x = -12.579745625 Solving 3.5 + x = -12.579745625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -12.579745625 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -12.579745625 + -3.5 x = -12.579745625 + -3.5 Combine like terms: -12.579745625 + -3.5 = -16.079745625 x = -16.079745625 Simplifying x = -16.079745625

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.079745625, -16.079745625}

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