0=x^2+28x+173

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Solution for 0=x^2+28x+173 equation:


Simplifying
0 = x2 + 28x + 173

Reorder the terms:
0 = 173 + 28x + x2

Solving
0 = 173 + 28x + x2

Solving for variable 'x'.

Combine like terms: 0 + -173 = -173
-173 + -28x + -1x2 = 173 + 28x + x2 + -173 + -28x + -1x2

Reorder the terms:
-173 + -28x + -1x2 = 173 + -173 + 28x + -28x + x2 + -1x2

Combine like terms: 173 + -173 = 0
-173 + -28x + -1x2 = 0 + 28x + -28x + x2 + -1x2
-173 + -28x + -1x2 = 28x + -28x + x2 + -1x2

Combine like terms: 28x + -28x = 0
-173 + -28x + -1x2 = 0 + x2 + -1x2
-173 + -28x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-173 + -28x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(173 + 28x + x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(173 + 28x + x2)' equal to zero and attempt to solve: Simplifying 173 + 28x + x2 = 0 Solving 173 + 28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-173' to each side of the equation. 173 + 28x + -173 + x2 = 0 + -173 Reorder the terms: 173 + -173 + 28x + x2 = 0 + -173 Combine like terms: 173 + -173 = 0 0 + 28x + x2 = 0 + -173 28x + x2 = 0 + -173 Combine like terms: 0 + -173 = -173 28x + x2 = -173 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -173 + 196 Reorder the terms: 196 + 28x + x2 = -173 + 196 Combine like terms: -173 + 196 = 23 196 + 28x + x2 = 23 Factor a perfect square on the left side: (x + 14)(x + 14) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 14) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + 14 = 4.795831523 Simplifying x + 14 = 4.795831523 Reorder the terms: 14 + x = 4.795831523 Solving 14 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 4.795831523 + -14 Combine like terms: 14 + -14 = 0 0 + x = 4.795831523 + -14 x = 4.795831523 + -14 Combine like terms: 4.795831523 + -14 = -9.204168477 x = -9.204168477 Simplifying x = -9.204168477

Subproblem 2

x + 14 = -4.795831523 Simplifying x + 14 = -4.795831523 Reorder the terms: 14 + x = -4.795831523 Solving 14 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -4.795831523 + -14 Combine like terms: 14 + -14 = 0 0 + x = -4.795831523 + -14 x = -4.795831523 + -14 Combine like terms: -4.795831523 + -14 = -18.795831523 x = -18.795831523 Simplifying x = -18.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-9.204168477, -18.795831523}

Solution

x = {-9.204168477, -18.795831523}

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