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Simplifying -1x2 + 65x + -1000 = 2 Reorder the terms: -1000 + 65x + -1x2 = 2 Solving -1000 + 65x + -1x2 = 2 Solving for variable 'x'. Reorder the terms: -1000 + -2 + 65x + -1x2 = 2 + -2 Combine like terms: -1000 + -2 = -1002 -1002 + 65x + -1x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -1002 + 65x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1002 + -65x + x2 = 0 Move the constant term to the right: Add '-1002' to each side of the equation. 1002 + -65x + -1002 + x2 = 0 + -1002 Reorder the terms: 1002 + -1002 + -65x + x2 = 0 + -1002 Combine like terms: 1002 + -1002 = 0 0 + -65x + x2 = 0 + -1002 -65x + x2 = 0 + -1002 Combine like terms: 0 + -1002 = -1002 -65x + x2 = -1002 The x term is -65x. Take half its coefficient (-32.5). Square it (1056.25) and add it to both sides. Add '1056.25' to each side of the equation. -65x + 1056.25 + x2 = -1002 + 1056.25 Reorder the terms: 1056.25 + -65x + x2 = -1002 + 1056.25 Combine like terms: -1002 + 1056.25 = 54.25 1056.25 + -65x + x2 = 54.25 Factor a perfect square on the left side: (x + -32.5)(x + -32.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x + -32.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x + -32.5 = 7.365459931 Simplifying x + -32.5 = 7.365459931 Reorder the terms: -32.5 + x = 7.365459931 Solving -32.5 + x = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = 7.365459931 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = 7.365459931 + 32.5 x = 7.365459931 + 32.5 Combine like terms: 7.365459931 + 32.5 = 39.865459931 x = 39.865459931 Simplifying x = 39.865459931Subproblem 2
x + -32.5 = -7.365459931 Simplifying x + -32.5 = -7.365459931 Reorder the terms: -32.5 + x = -7.365459931 Solving -32.5 + x = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32.5' to each side of the equation. -32.5 + 32.5 + x = -7.365459931 + 32.5 Combine like terms: -32.5 + 32.5 = 0.0 0.0 + x = -7.365459931 + 32.5 x = -7.365459931 + 32.5 Combine like terms: -7.365459931 + 32.5 = 25.134540069 x = 25.134540069 Simplifying x = 25.134540069Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.865459931, 25.134540069}
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