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Simplifying x(x + 1) = 29 Reorder the terms: x(1 + x) = 29 (1 * x + x * x) = 29 (1x + x2) = 29 Solving 1x + x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 1x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 1x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 1x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 1x + x2 = 0 + 29 1x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 1x + x2 = 29 The x term is 1x. 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 = 29 + 0.25 Reorder the terms: 0.25 + x + x2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 0.25 + x + x2 = 29.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + 0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + 0.5 = 5.408326913 Simplifying x + 0.5 = 5.408326913 Reorder the terms: 0.5 + x = 5.408326913 Solving 0.5 + x = 5.408326913 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 = 5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.408326913 + -0.5 x = 5.408326913 + -0.5 Combine like terms: 5.408326913 + -0.5 = 4.908326913 x = 4.908326913 Simplifying x = 4.908326913Subproblem 2
x + 0.5 = -5.408326913 Simplifying x + 0.5 = -5.408326913 Reorder the terms: 0.5 + x = -5.408326913 Solving 0.5 + x = -5.408326913 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 = -5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.408326913 + -0.5 x = -5.408326913 + -0.5 Combine like terms: -5.408326913 + -0.5 = -5.908326913 x = -5.908326913 Simplifying x = -5.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.908326913, -5.908326913}
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