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Simplifying -0.5x2 + 40x + 400 = 403 Reorder the terms: 400 + 40x + -0.5x2 = 403 Solving 400 + 40x + -0.5x2 = 403 Solving for variable 'x'. Reorder the terms: 400 + -403 + 40x + -0.5x2 = 403 + -403 Combine like terms: 400 + -403 = -3 -3 + 40x + -0.5x2 = 403 + -403 Combine like terms: 403 + -403 = 0 -3 + 40x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 6 + -80x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -80x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -80x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -80x + x2 = 0 + -6 -80x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -80x + x2 = -6 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -6 + 1600 Reorder the terms: 1600 + -80x + x2 = -6 + 1600 Combine like terms: -6 + 1600 = 1594 1600 + -80x + x2 = 1594 Factor a perfect square on the left side: (x + -40)(x + -40) = 1594 Calculate the square root of the right side: 39.924929555 Break this problem into two subproblems by setting (x + -40) equal to 39.924929555 and -39.924929555.Subproblem 1
x + -40 = 39.924929555 Simplifying x + -40 = 39.924929555 Reorder the terms: -40 + x = 39.924929555 Solving -40 + x = 39.924929555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.924929555 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.924929555 + 40 x = 39.924929555 + 40 Combine like terms: 39.924929555 + 40 = 79.924929555 x = 79.924929555 Simplifying x = 79.924929555Subproblem 2
x + -40 = -39.924929555 Simplifying x + -40 = -39.924929555 Reorder the terms: -40 + x = -39.924929555 Solving -40 + x = -39.924929555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.924929555 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.924929555 + 40 x = -39.924929555 + 40 Combine like terms: -39.924929555 + 40 = 0.075070445 x = 0.075070445 Simplifying x = 0.075070445Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.924929555, 0.075070445}
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