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Simplifying 0.40x(0.50x) + -0.50x = 500 Remove parenthesis around (0.50x) 0.40x * 0.50x + -0.50x = 500 Reorder the terms for easier multiplication: 0.40 * 0.50x * x + -0.50x = 500 Multiply 0.40 * 0.50 0.2x * x + -0.50x = 500 Multiply x * x 0.2x2 + -0.50x = 500 Reorder the terms: -0.50x + 0.2x2 = 500 Solving -0.50x + 0.2x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + -0.50x + 0.2x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + -0.50x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -2500 + -2.5x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + -2.5x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + -2.5x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + -2.5x + x2 = 0 + 2500 -2.5x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 -2.5x + x2 = 2500 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 2500 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 2500 + 1.5625 Combine like terms: 2500 + 1.5625 = 2501.5625 1.5625 + -2.5x + x2 = 2501.5625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 2501.5625 Calculate the square root of the right side: 50.015622559 Break this problem into two subproblems by setting (x + -1.25) equal to 50.015622559 and -50.015622559.Subproblem 1
x + -1.25 = 50.015622559 Simplifying x + -1.25 = 50.015622559 Reorder the terms: -1.25 + x = 50.015622559 Solving -1.25 + x = 50.015622559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 50.015622559 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 50.015622559 + 1.25 x = 50.015622559 + 1.25 Combine like terms: 50.015622559 + 1.25 = 51.265622559 x = 51.265622559 Simplifying x = 51.265622559Subproblem 2
x + -1.25 = -50.015622559 Simplifying x + -1.25 = -50.015622559 Reorder the terms: -1.25 + x = -50.015622559 Solving -1.25 + x = -50.015622559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -50.015622559 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -50.015622559 + 1.25 x = -50.015622559 + 1.25 Combine like terms: -50.015622559 + 1.25 = -48.765622559 x = -48.765622559 Simplifying x = -48.765622559Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.265622559, -48.765622559}
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