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Simplifying x2 + x = 3375 Reorder the terms: x + x2 = 3375 Solving x + x2 = 3375 Solving for variable 'x'. Reorder the terms: -3375 + x + x2 = 3375 + -3375 Combine like terms: 3375 + -3375 = 0 -3375 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3375' to each side of the equation. -3375 + x + 3375 + x2 = 0 + 3375 Reorder the terms: -3375 + 3375 + x + x2 = 0 + 3375 Combine like terms: -3375 + 3375 = 0 0 + x + x2 = 0 + 3375 x + x2 = 0 + 3375 Combine like terms: 0 + 3375 = 3375 x + x2 = 3375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 3375 + 0.25 Reorder the terms: 0.25 + x + x2 = 3375 + 0.25 Combine like terms: 3375 + 0.25 = 3375.25 0.25 + x + x2 = 3375.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3375.25 Calculate the square root of the right side: 58.096901811 Break this problem into two subproblems by setting (x + 0.5) equal to 58.096901811 and -58.096901811.Subproblem 1
x + 0.5 = 58.096901811 Simplifying x + 0.5 = 58.096901811 Reorder the terms: 0.5 + x = 58.096901811 Solving 0.5 + x = 58.096901811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 58.096901811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 58.096901811 + -0.5 x = 58.096901811 + -0.5 Combine like terms: 58.096901811 + -0.5 = 57.596901811 x = 57.596901811 Simplifying x = 57.596901811Subproblem 2
x + 0.5 = -58.096901811 Simplifying x + 0.5 = -58.096901811 Reorder the terms: 0.5 + x = -58.096901811 Solving 0.5 + x = -58.096901811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -58.096901811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -58.096901811 + -0.5 x = -58.096901811 + -0.5 Combine like terms: -58.096901811 + -0.5 = -58.596901811 x = -58.596901811 Simplifying x = -58.596901811Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.596901811, -58.596901811}
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