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Simplifying X * X + 5X = 60 Multiply X * X X2 + 5X = 60 Reorder the terms: 5X + X2 = 60 Solving 5X + X2 = 60 Solving for variable 'X'. Reorder the terms: -60 + 5X + X2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 5X + 60 + X2 = 0 + 60 Reorder the terms: -60 + 60 + 5X + X2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 5X + X2 = 0 + 60 5X + X2 = 0 + 60 Combine like terms: 0 + 60 = 60 5X + X2 = 60 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 = 60 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 60 + 6.25 Combine like terms: 60 + 6.25 = 66.25 6.25 + 5X + X2 = 66.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 66.25 Calculate the square root of the right side: 8.139410298 Break this problem into two subproblems by setting (X + 2.5) equal to 8.139410298 and -8.139410298.Subproblem 1
X + 2.5 = 8.139410298 Simplifying X + 2.5 = 8.139410298 Reorder the terms: 2.5 + X = 8.139410298 Solving 2.5 + X = 8.139410298 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 = 8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 8.139410298 + -2.5 X = 8.139410298 + -2.5 Combine like terms: 8.139410298 + -2.5 = 5.639410298 X = 5.639410298 Simplifying X = 5.639410298Subproblem 2
X + 2.5 = -8.139410298 Simplifying X + 2.5 = -8.139410298 Reorder the terms: 2.5 + X = -8.139410298 Solving 2.5 + X = -8.139410298 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 = -8.139410298 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -8.139410298 + -2.5 X = -8.139410298 + -2.5 Combine like terms: -8.139410298 + -2.5 = -10.639410298 X = -10.639410298 Simplifying X = -10.639410298Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.639410298, -10.639410298}
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