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Simplifying x2 + x = 101 Reorder the terms: x + x2 = 101 Solving x + x2 = 101 Solving for variable 'x'. Reorder the terms: -101 + x + x2 = 101 + -101 Combine like terms: 101 + -101 = 0 -101 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + x + 101 + x2 = 0 + 101 Reorder the terms: -101 + 101 + x + x2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + x + x2 = 0 + 101 x + x2 = 0 + 101 Combine like terms: 0 + 101 = 101 x + x2 = 101 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 = 101 + 0.25 Reorder the terms: 0.25 + x + x2 = 101 + 0.25 Combine like terms: 101 + 0.25 = 101.25 0.25 + x + x2 = 101.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + 0.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + 0.5 = 10.062305899 Simplifying x + 0.5 = 10.062305899 Reorder the terms: 0.5 + x = 10.062305899 Solving 0.5 + x = 10.062305899 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 = 10.062305899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.062305899 + -0.5 x = 10.062305899 + -0.5 Combine like terms: 10.062305899 + -0.5 = 9.562305899 x = 9.562305899 Simplifying x = 9.562305899Subproblem 2
x + 0.5 = -10.062305899 Simplifying x + 0.5 = -10.062305899 Reorder the terms: 0.5 + x = -10.062305899 Solving 0.5 + x = -10.062305899 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 = -10.062305899 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.062305899 + -0.5 x = -10.062305899 + -0.5 Combine like terms: -10.062305899 + -0.5 = -10.562305899 x = -10.562305899 Simplifying x = -10.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.562305899, -10.562305899}
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