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Simplifying x(x + -100) = 2100 Reorder the terms: x(-100 + x) = 2100 (-100 * x + x * x) = 2100 (-100x + x2) = 2100 Solving -100x + x2 = 2100 Solving for variable 'x'. Reorder the terms: -2100 + -100x + x2 = 2100 + -2100 Combine like terms: 2100 + -2100 = 0 -2100 + -100x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2100' to each side of the equation. -2100 + -100x + 2100 + x2 = 0 + 2100 Reorder the terms: -2100 + 2100 + -100x + x2 = 0 + 2100 Combine like terms: -2100 + 2100 = 0 0 + -100x + x2 = 0 + 2100 -100x + x2 = 0 + 2100 Combine like terms: 0 + 2100 = 2100 -100x + x2 = 2100 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 2100 + 2500 Reorder the terms: 2500 + -100x + x2 = 2100 + 2500 Combine like terms: 2100 + 2500 = 4600 2500 + -100x + x2 = 4600 Factor a perfect square on the left side: (x + -50)(x + -50) = 4600 Calculate the square root of the right side: 67.823299831 Break this problem into two subproblems by setting (x + -50) equal to 67.823299831 and -67.823299831.Subproblem 1
x + -50 = 67.823299831 Simplifying x + -50 = 67.823299831 Reorder the terms: -50 + x = 67.823299831 Solving -50 + x = 67.823299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 67.823299831 + 50 Combine like terms: -50 + 50 = 0 0 + x = 67.823299831 + 50 x = 67.823299831 + 50 Combine like terms: 67.823299831 + 50 = 117.823299831 x = 117.823299831 Simplifying x = 117.823299831Subproblem 2
x + -50 = -67.823299831 Simplifying x + -50 = -67.823299831 Reorder the terms: -50 + x = -67.823299831 Solving -50 + x = -67.823299831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -67.823299831 + 50 Combine like terms: -50 + 50 = 0 0 + x = -67.823299831 + 50 x = -67.823299831 + 50 Combine like terms: -67.823299831 + 50 = -17.823299831 x = -17.823299831 Simplifying x = -17.823299831Solution
The solution to the problem is based on the solutions from the subproblems. x = {117.823299831, -17.823299831}
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