2x^2+5x=173

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Solution for 2x^2+5x=173 equation:


Simplifying
2x2 + 5x = 173

Reorder the terms:
5x + 2x2 = 173

Solving
5x + 2x2 = 173

Solving for variable 'x'.

Reorder the terms:
-173 + 5x + 2x2 = 173 + -173

Combine like terms: 173 + -173 = 0
-173 + 5x + 2x2 = 0

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

Divide each side by '2'.
-86.5 + 2.5x + x2 = 0

Move the constant term to the right:

Add '86.5' to each side of the equation.
-86.5 + 2.5x + 86.5 + x2 = 0 + 86.5

Reorder the terms:
-86.5 + 86.5 + 2.5x + x2 = 0 + 86.5

Combine like terms: -86.5 + 86.5 = 0.0
0.0 + 2.5x + x2 = 0 + 86.5
2.5x + x2 = 0 + 86.5

Combine like terms: 0 + 86.5 = 86.5
2.5x + x2 = 86.5

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 86.5 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 86.5 + 1.5625

Combine like terms: 86.5 + 1.5625 = 88.0625
1.5625 + 2.5x + x2 = 88.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 88.0625

Calculate the square root of the right side: 9.38416219

Break this problem into two subproblems by setting 
(x + 1.25) equal to 9.38416219 and -9.38416219.

Subproblem 1

x + 1.25 = 9.38416219 Simplifying x + 1.25 = 9.38416219 Reorder the terms: 1.25 + x = 9.38416219 Solving 1.25 + x = 9.38416219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 9.38416219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 9.38416219 + -1.25 x = 9.38416219 + -1.25 Combine like terms: 9.38416219 + -1.25 = 8.13416219 x = 8.13416219 Simplifying x = 8.13416219

Subproblem 2

x + 1.25 = -9.38416219 Simplifying x + 1.25 = -9.38416219 Reorder the terms: 1.25 + x = -9.38416219 Solving 1.25 + x = -9.38416219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -9.38416219 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -9.38416219 + -1.25 x = -9.38416219 + -1.25 Combine like terms: -9.38416219 + -1.25 = -10.63416219 x = -10.63416219 Simplifying x = -10.63416219

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.13416219, -10.63416219}

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