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Simplifying (3x2) + -1.5x + -5 = 0 Reorder the terms: -5 + -1.5x + (3x2) = 0 Solving -5 + -1.5x + (3x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.666666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -0.5x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -0.5x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 1.666666667 -0.5x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -0.5x + x2 = 1.666666667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.666666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.666666667 + 0.0625 Combine like terms: 1.666666667 + 0.0625 = 1.729166667 0.0625 + -0.5x + x2 = 1.729166667 Factor a perfect square on the left side: ((x) + -0.25)((x) + -0.25) = 1.729166667 Calculate the square root of the right side: 1.31497782 Break this problem into two subproblems by setting ((x) + -0.25) equal to 1.31497782 and -1.31497782.Subproblem 1
(x) + -0.25 = 1.31497782 Simplifying (x) + -0.25 = 1.31497782 x + -0.25 = 1.31497782 Reorder the terms: -0.25 + x = 1.31497782 Solving -0.25 + x = 1.31497782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.31497782 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.31497782 + 0.25 x = 1.31497782 + 0.25 Combine like terms: 1.31497782 + 0.25 = 1.56497782 x = 1.56497782 Simplifying x = 1.56497782Subproblem 2
(x) + -0.25 = -1.31497782 Simplifying (x) + -0.25 = -1.31497782 x + -0.25 = -1.31497782 Reorder the terms: -0.25 + x = -1.31497782 Solving -0.25 + x = -1.31497782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.31497782 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.31497782 + 0.25 x = -1.31497782 + 0.25 Combine like terms: -1.31497782 + 0.25 = -1.06497782 x = -1.06497782 Simplifying x = -1.06497782Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.56497782, -1.06497782}
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