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Simplifying 0.5x2 + -0.75x + -0.5 = 0 Reorder the terms: -0.5 + -0.75x + 0.5x2 = 0 Solving -0.5 + -0.75x + 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'. -1 + -1.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.5x + x2 = 0 + 1 -1.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.5x + x2 = 1 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 1 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 1 + 0.5625 Combine like terms: 1 + 0.5625 = 1.5625 0.5625 + -1.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + -0.75) equal to 1.25 and -1.25.Subproblem 1
x + -0.75 = 1.25 Simplifying x + -0.75 = 1.25 Reorder the terms: -0.75 + x = 1.25 Solving -0.75 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.25 + 0.75 x = 1.25 + 0.75 Combine like terms: 1.25 + 0.75 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.75 = -1.25 Simplifying x + -0.75 = -1.25 Reorder the terms: -0.75 + x = -1.25 Solving -0.75 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.25 + 0.75 x = -1.25 + 0.75 Combine like terms: -1.25 + 0.75 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.5}
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