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Simplifying 36.5 = 0.04x2 + -1x Reorder the terms: 36.5 = -1x + 0.04x2 Solving 36.5 = -1x + 0.04x2 Solving for variable 'x'. Reorder the terms: 36.5 + x + -0.04x2 = -1x + x + 0.04x2 + -0.04x2 Combine like terms: -1x + x = 0 36.5 + x + -0.04x2 = 0 + 0.04x2 + -0.04x2 36.5 + x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 36.5 + x + -0.04x2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -912.5 + -25x + x2 = 0 Move the constant term to the right: Add '912.5' to each side of the equation. -912.5 + -25x + 912.5 + x2 = 0 + 912.5 Reorder the terms: -912.5 + 912.5 + -25x + x2 = 0 + 912.5 Combine like terms: -912.5 + 912.5 = 0.0 0.0 + -25x + x2 = 0 + 912.5 -25x + x2 = 0 + 912.5 Combine like terms: 0 + 912.5 = 912.5 -25x + x2 = 912.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -25x + 0.25 + x2 = 912.5 + 0.25 Reorder the terms: 0.25 + -25x + x2 = 912.5 + 0.25 Combine like terms: 912.5 + 0.25 = 912.75 0.25 + -25x + x2 = 912.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 912.75 Calculate the square root of the right side: 30.21175268 Break this problem into two subproblems by setting (x + 0.5) equal to 30.21175268 and -30.21175268.Subproblem 1
x + 0.5 = 30.21175268 Simplifying x + 0.5 = 30.21175268 Reorder the terms: 0.5 + x = 30.21175268 Solving 0.5 + x = 30.21175268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 30.21175268 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 30.21175268 + -0.5 x = 30.21175268 + -0.5 Combine like terms: 30.21175268 + -0.5 = 29.71175268 x = 29.71175268 Simplifying x = 29.71175268Subproblem 2
x + 0.5 = -30.21175268 Simplifying x + 0.5 = -30.21175268 Reorder the terms: 0.5 + x = -30.21175268 Solving 0.5 + x = -30.21175268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -30.21175268 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -30.21175268 + -0.5 x = -30.21175268 + -0.5 Combine like terms: -30.21175268 + -0.5 = -30.71175268 x = -30.71175268 Simplifying x = -30.71175268Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.71175268, -30.71175268}
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