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Simplifying 5x + x2 + -186 = 0 Reorder the terms: -186 + 5x + x2 = 0 Solving -186 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '186' to each side of the equation. -186 + 5x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + 5x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + 5x + x2 = 0 + 186 5x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 5x + x2 = 186 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 186 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 186 + 6.25 Combine like terms: 186 + 6.25 = 192.25 6.25 + 5x + x2 = 192.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (x + 2.5) equal to 13.865424624 and -13.865424624.Subproblem 1
x + 2.5 = 13.865424624 Simplifying x + 2.5 = 13.865424624 Reorder the terms: 2.5 + x = 13.865424624 Solving 2.5 + x = 13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 13.865424624 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.865424624 + -2.5 x = 13.865424624 + -2.5 Combine like terms: 13.865424624 + -2.5 = 11.365424624 x = 11.365424624 Simplifying x = 11.365424624Subproblem 2
x + 2.5 = -13.865424624 Simplifying x + 2.5 = -13.865424624 Reorder the terms: 2.5 + x = -13.865424624 Solving 2.5 + x = -13.865424624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -13.865424624 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.865424624 + -2.5 x = -13.865424624 + -2.5 Combine like terms: -13.865424624 + -2.5 = -16.365424624 x = -16.365424624 Simplifying x = -16.365424624Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.365424624, -16.365424624}
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