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Simplifying x2 + -29x + 200 = 0 Reorder the terms: 200 + -29x + x2 = 0 Solving 200 + -29x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-200' to each side of the equation. 200 + -29x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -29x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -29x + x2 = 0 + -200 -29x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -29x + x2 = -200 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -200 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -200 + 210.25 Combine like terms: -200 + 210.25 = 10.25 210.25 + -29x + x2 = 10.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -14.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -14.5 = 3.201562119 Simplifying x + -14.5 = 3.201562119 Reorder the terms: -14.5 + x = 3.201562119 Solving -14.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 3.201562119 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 3.201562119 + 14.5 x = 3.201562119 + 14.5 Combine like terms: 3.201562119 + 14.5 = 17.701562119 x = 17.701562119 Simplifying x = 17.701562119Subproblem 2
x + -14.5 = -3.201562119 Simplifying x + -14.5 = -3.201562119 Reorder the terms: -14.5 + x = -3.201562119 Solving -14.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -3.201562119 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -3.201562119 + 14.5 x = -3.201562119 + 14.5 Combine like terms: -3.201562119 + 14.5 = 11.298437881 x = 11.298437881 Simplifying x = 11.298437881Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.701562119, 11.298437881}
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