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Simplifying x2 + x = 840 Reorder the terms: x + x2 = 840 Solving x + x2 = 840 Solving for variable 'x'. Reorder the terms: -840 + x + x2 = 840 + -840 Combine like terms: 840 + -840 = 0 -840 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '840' to each side of the equation. -840 + x + 840 + x2 = 0 + 840 Reorder the terms: -840 + 840 + x + x2 = 0 + 840 Combine like terms: -840 + 840 = 0 0 + x + x2 = 0 + 840 x + x2 = 0 + 840 Combine like terms: 0 + 840 = 840 x + x2 = 840 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 = 840 + 0.25 Reorder the terms: 0.25 + x + x2 = 840 + 0.25 Combine like terms: 840 + 0.25 = 840.25 0.25 + x + x2 = 840.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 840.25 Calculate the square root of the right side: 28.987066081 Break this problem into two subproblems by setting (x + 0.5) equal to 28.987066081 and -28.987066081.Subproblem 1
x + 0.5 = 28.987066081 Simplifying x + 0.5 = 28.987066081 Reorder the terms: 0.5 + x = 28.987066081 Solving 0.5 + x = 28.987066081 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 = 28.987066081 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 28.987066081 + -0.5 x = 28.987066081 + -0.5 Combine like terms: 28.987066081 + -0.5 = 28.487066081 x = 28.487066081 Simplifying x = 28.487066081Subproblem 2
x + 0.5 = -28.987066081 Simplifying x + 0.5 = -28.987066081 Reorder the terms: 0.5 + x = -28.987066081 Solving 0.5 + x = -28.987066081 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 = -28.987066081 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -28.987066081 + -0.5 x = -28.987066081 + -0.5 Combine like terms: -28.987066081 + -0.5 = -29.487066081 x = -29.487066081 Simplifying x = -29.487066081Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.487066081, -29.487066081}
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