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Simplifying x2 + 5x = 155 Reorder the terms: 5x + x2 = 155 Solving 5x + x2 = 155 Solving for variable 'x'. Reorder the terms: -155 + 5x + x2 = 155 + -155 Combine like terms: 155 + -155 = 0 -155 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + 5x + 155 + x2 = 0 + 155 Reorder the terms: -155 + 155 + 5x + x2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + 5x + x2 = 0 + 155 5x + x2 = 0 + 155 Combine like terms: 0 + 155 = 155 5x + x2 = 155 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 = 155 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 155 + 6.25 Combine like terms: 155 + 6.25 = 161.25 6.25 + 5x + x2 = 161.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (x + 2.5) equal to 12.698425099 and -12.698425099.Subproblem 1
x + 2.5 = 12.698425099 Simplifying x + 2.5 = 12.698425099 Reorder the terms: 2.5 + x = 12.698425099 Solving 2.5 + x = 12.698425099 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 = 12.698425099 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.698425099 + -2.5 x = 12.698425099 + -2.5 Combine like terms: 12.698425099 + -2.5 = 10.198425099 x = 10.198425099 Simplifying x = 10.198425099Subproblem 2
x + 2.5 = -12.698425099 Simplifying x + 2.5 = -12.698425099 Reorder the terms: 2.5 + x = -12.698425099 Solving 2.5 + x = -12.698425099 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 = -12.698425099 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.698425099 + -2.5 x = -12.698425099 + -2.5 Combine like terms: -12.698425099 + -2.5 = -15.198425099 x = -15.198425099 Simplifying x = -15.198425099Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.198425099, -15.198425099}
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