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Simplifying (0.5x2) + -1(1.25x) + -3 = 0 Remove parenthesis around (1.25x) (0.5x2) + -1 * 1.25x + -3 = 0 Multiply -1 * 1.25 (0.5x2) + -1.25x + -3 = 0 Reorder the terms: -3 + -1.25x + (0.5x2) = 0 Solving -3 + -1.25x + (0.5x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -6 + -2.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -2.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -2.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2.5x + x2 = 0 + 6 -2.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2.5x + x2 = 6 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 = 6 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6 + 1.5625 Combine like terms: 6 + 1.5625 = 7.5625 1.5625 + -2.5x + x2 = 7.5625 Factor a perfect square on the left side: ((x) + -1.25)((x) + -1.25) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting ((x) + -1.25) equal to 2.75 and -2.75.Subproblem 1
(x) + -1.25 = 2.75 Simplifying (x) + -1.25 = 2.75 x + -1.25 = 2.75 Reorder the terms: -1.25 + x = 2.75 Solving -1.25 + x = 2.75 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 = 2.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.75 + 1.25 x = 2.75 + 1.25 Combine like terms: 2.75 + 1.25 = 4 x = 4 Simplifying x = 4Subproblem 2
(x) + -1.25 = -2.75 Simplifying (x) + -1.25 = -2.75 x + -1.25 = -2.75 Reorder the terms: -1.25 + x = -2.75 Solving -1.25 + x = -2.75 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 = -2.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.75 + 1.25 x = -2.75 + 1.25 Combine like terms: -2.75 + 1.25 = -1.5 x = -1.5 Simplifying x = -1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -1.5}
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