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Simplifying (0.5x2) + -1(1.25x) + -3 = 3 Remove parenthesis around (1.25x) (0.5x2) + -1 * 1.25x + -3 = 3 Multiply -1 * 1.25 (0.5x2) + -1.25x + -3 = 3 Reorder the terms: -3 + -1.25x + (0.5x2) = 3 Solving -3 + -1.25x + (0.5x2) = 3 Solving for variable 'x'. Reorder the terms: -3 + -3 + -1.25x + (0.5x2) = 3 + -3 Combine like terms: -3 + -3 = -6 -6 + -1.25x + (0.5x2) = 3 + -3 Combine like terms: 3 + -3 = 0 -6 + -1.25x + (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'. -12 + -2.5x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -2.5x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -2.5x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -2.5x + x2 = 0 + 12 -2.5x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -2.5x + x2 = 12 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 = 12 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 12 + 1.5625 Combine like terms: 12 + 1.5625 = 13.5625 1.5625 + -2.5x + x2 = 13.5625 Factor a perfect square on the left side: ((x) + -1.25)((x) + -1.25) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting ((x) + -1.25) equal to 3.682729966 and -3.682729966.Subproblem 1
(x) + -1.25 = 3.682729966 Simplifying (x) + -1.25 = 3.682729966 x + -1.25 = 3.682729966 Reorder the terms: -1.25 + x = 3.682729966 Solving -1.25 + x = 3.682729966 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 = 3.682729966 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.682729966 + 1.25 x = 3.682729966 + 1.25 Combine like terms: 3.682729966 + 1.25 = 4.932729966 x = 4.932729966 Simplifying x = 4.932729966Subproblem 2
(x) + -1.25 = -3.682729966 Simplifying (x) + -1.25 = -3.682729966 x + -1.25 = -3.682729966 Reorder the terms: -1.25 + x = -3.682729966 Solving -1.25 + x = -3.682729966 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 = -3.682729966 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.682729966 + 1.25 x = -3.682729966 + 1.25 Combine like terms: -3.682729966 + 1.25 = -2.432729966 x = -2.432729966 Simplifying x = -2.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.932729966, -2.432729966}
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