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Simplifying 500 = x2 + 100x + -1600 Reorder the terms: 500 = -1600 + 100x + x2 Solving 500 = -1600 + 100x + x2 Solving for variable 'x'. Combine like terms: 500 + 1600 = 2100 2100 + -100x + -1x2 = -1600 + 100x + x2 + 1600 + -100x + -1x2 Reorder the terms: 2100 + -100x + -1x2 = -1600 + 1600 + 100x + -100x + x2 + -1x2 Combine like terms: -1600 + 1600 = 0 2100 + -100x + -1x2 = 0 + 100x + -100x + x2 + -1x2 2100 + -100x + -1x2 = 100x + -100x + x2 + -1x2 Combine like terms: 100x + -100x = 0 2100 + -100x + -1x2 = 0 + x2 + -1x2 2100 + -100x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2100 + -100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2100 + 100x + x2 = 0 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 = 17.823299831 x = 17.823299831 Simplifying x = 17.823299831Subproblem 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 = -117.823299831 x = -117.823299831 Simplifying x = -117.823299831Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.823299831, -117.823299831}
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