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Simplifying 40 = 0.01x2 + 0.5x + 2 Reorder the terms: 40 = 2 + 0.5x + 0.01x2 Solving 40 = 2 + 0.5x + 0.01x2 Solving for variable 'x'. Combine like terms: 40 + -2 = 38 38 + -0.5x + -0.01x2 = 2 + 0.5x + 0.01x2 + -2 + -0.5x + -0.01x2 Reorder the terms: 38 + -0.5x + -0.01x2 = 2 + -2 + 0.5x + -0.5x + 0.01x2 + -0.01x2 Combine like terms: 2 + -2 = 0 38 + -0.5x + -0.01x2 = 0 + 0.5x + -0.5x + 0.01x2 + -0.01x2 38 + -0.5x + -0.01x2 = 0.5x + -0.5x + 0.01x2 + -0.01x2 Combine like terms: 0.5x + -0.5x = 0.0 38 + -0.5x + -0.01x2 = 0.0 + 0.01x2 + -0.01x2 38 + -0.5x + -0.01x2 = 0.01x2 + -0.01x2 Combine like terms: 0.01x2 + -0.01x2 = 0.00 38 + -0.5x + -0.01x2 = 0.00 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -3800 + 50x + x2 = 0 Move the constant term to the right: Add '3800' to each side of the equation. -3800 + 50x + 3800 + x2 = 0 + 3800 Reorder the terms: -3800 + 3800 + 50x + x2 = 0 + 3800 Combine like terms: -3800 + 3800 = 0 0 + 50x + x2 = 0 + 3800 50x + x2 = 0 + 3800 Combine like terms: 0 + 3800 = 3800 50x + x2 = 3800 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 3800 + 625 Reorder the terms: 625 + 50x + x2 = 3800 + 625 Combine like terms: 3800 + 625 = 4425 625 + 50x + x2 = 4425 Factor a perfect square on the left side: (x + 25)(x + 25) = 4425 Calculate the square root of the right side: 66.520673478 Break this problem into two subproblems by setting (x + 25) equal to 66.520673478 and -66.520673478.Subproblem 1
x + 25 = 66.520673478 Simplifying x + 25 = 66.520673478 Reorder the terms: 25 + x = 66.520673478 Solving 25 + x = 66.520673478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 66.520673478 + -25 Combine like terms: 25 + -25 = 0 0 + x = 66.520673478 + -25 x = 66.520673478 + -25 Combine like terms: 66.520673478 + -25 = 41.520673478 x = 41.520673478 Simplifying x = 41.520673478Subproblem 2
x + 25 = -66.520673478 Simplifying x + 25 = -66.520673478 Reorder the terms: 25 + x = -66.520673478 Solving 25 + x = -66.520673478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -66.520673478 + -25 Combine like terms: 25 + -25 = 0 0 + x = -66.520673478 + -25 x = -66.520673478 + -25 Combine like terms: -66.520673478 + -25 = -91.520673478 x = -91.520673478 Simplifying x = -91.520673478Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.520673478, -91.520673478}
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