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Simplifying 0.50x + -0.20x(40 + x) = -0.05(40) 0.50x + (40 * -0.20x + x * -0.20x) = -0.05(40) 0.50x + (-8x + -0.20x2) = -0.05(40) Combine like terms: 0.50x + -8x = -7.5x -7.5x + -0.20x2 = -0.05(40) Multiply -0.05 * 40 -7.5x + -0.20x2 = -2 Solving -7.5x + -0.20x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -7.5x + -0.20x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -7.5x + -0.20x2 = 0 Begin completing the square. Divide all terms by -0.20 the coefficient of the squared term: Divide each side by '-0.20'. -10 + 37.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 37.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 37.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 37.5x + x2 = 0 + 10 37.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 37.5x + x2 = 10 The x term is 37.5x. Take half its coefficient (18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. 37.5x + 351.5625 + x2 = 10 + 351.5625 Reorder the terms: 351.5625 + 37.5x + x2 = 10 + 351.5625 Combine like terms: 10 + 351.5625 = 361.5625 351.5625 + 37.5x + x2 = 361.5625 Factor a perfect square on the left side: (x + 18.75)(x + 18.75) = 361.5625 Calculate the square root of the right side: 19.01479687 Break this problem into two subproblems by setting (x + 18.75) equal to 19.01479687 and -19.01479687.Subproblem 1
x + 18.75 = 19.01479687 Simplifying x + 18.75 = 19.01479687 Reorder the terms: 18.75 + x = 19.01479687 Solving 18.75 + x = 19.01479687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = 19.01479687 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = 19.01479687 + -18.75 x = 19.01479687 + -18.75 Combine like terms: 19.01479687 + -18.75 = 0.26479687 x = 0.26479687 Simplifying x = 0.26479687Subproblem 2
x + 18.75 = -19.01479687 Simplifying x + 18.75 = -19.01479687 Reorder the terms: 18.75 + x = -19.01479687 Solving 18.75 + x = -19.01479687 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.75' to each side of the equation. 18.75 + -18.75 + x = -19.01479687 + -18.75 Combine like terms: 18.75 + -18.75 = 0.00 0.00 + x = -19.01479687 + -18.75 x = -19.01479687 + -18.75 Combine like terms: -19.01479687 + -18.75 = -37.76479687 x = -37.76479687 Simplifying x = -37.76479687Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26479687, -37.76479687}
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