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Simplifying 100 = x2 + 10x Reorder the terms: 100 = 10x + x2 Solving 100 = 10x + x2 Solving for variable 'x'. Reorder the terms: 100 + -10x + -1x2 = 10x + -10x + x2 + -1x2 Combine like terms: 10x + -10x = 0 100 + -10x + -1x2 = 0 + x2 + -1x2 100 + -10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 100 + -10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -100 + 10x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 10x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 10x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 10x + x2 = 0 + 100 10x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 10x + x2 = 100 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 100 + 25 Reorder the terms: 25 + 10x + x2 = 100 + 25 Combine like terms: 100 + 25 = 125 25 + 10x + x2 = 125 Factor a perfect square on the left side: (x + 5)(x + 5) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (x + 5) equal to 11.180339887 and -11.180339887.Subproblem 1
x + 5 = 11.180339887 Simplifying x + 5 = 11.180339887 Reorder the terms: 5 + x = 11.180339887 Solving 5 + x = 11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = 11.180339887 + -5 x = 11.180339887 + -5 Combine like terms: 11.180339887 + -5 = 6.180339887 x = 6.180339887 Simplifying x = 6.180339887Subproblem 2
x + 5 = -11.180339887 Simplifying x + 5 = -11.180339887 Reorder the terms: 5 + x = -11.180339887 Solving 5 + x = -11.180339887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + x = -11.180339887 + -5 x = -11.180339887 + -5 Combine like terms: -11.180339887 + -5 = -16.180339887 x = -16.180339887 Simplifying x = -16.180339887Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.180339887, -16.180339887}
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