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Simplifying 0.5x2 + -1.5x + 0.075 = 0 Reorder the terms: 0.075 + -1.5x + 0.5x2 = 0 Solving 0.075 + -1.5x + 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'. 0.15 + -3x + x2 = 0 Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -3x + -0.15 + x2 = 0 + -0.15 Reorder the terms: 0.15 + -0.15 + -3x + x2 = 0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -3x + x2 = 0 + -0.15 -3x + x2 = 0 + -0.15 Combine like terms: 0 + -0.15 = -0.15 -3x + x2 = -0.15 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.15 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.15 + 2.25 Combine like terms: -0.15 + 2.25 = 2.1 2.25 + -3x + x2 = 2.1 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.1 Calculate the square root of the right side: 1.449137675 Break this problem into two subproblems by setting (x + -1.5) equal to 1.449137675 and -1.449137675.Subproblem 1
x + -1.5 = 1.449137675 Simplifying x + -1.5 = 1.449137675 Reorder the terms: -1.5 + x = 1.449137675 Solving -1.5 + x = 1.449137675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.449137675 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.449137675 + 1.5 x = 1.449137675 + 1.5 Combine like terms: 1.449137675 + 1.5 = 2.949137675 x = 2.949137675 Simplifying x = 2.949137675Subproblem 2
x + -1.5 = -1.449137675 Simplifying x + -1.5 = -1.449137675 Reorder the terms: -1.5 + x = -1.449137675 Solving -1.5 + x = -1.449137675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.449137675 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.449137675 + 1.5 x = -1.449137675 + 1.5 Combine like terms: -1.449137675 + 1.5 = 0.050862325 x = 0.050862325 Simplifying x = 0.050862325Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.949137675, 0.050862325}
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