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Simplifying 0.55x2 + -1.066x = 1.5 Reorder the terms: -1.066x + 0.55x2 = 1.5 Solving -1.066x + 0.55x2 = 1.5 Solving for variable 'x'. Reorder the terms: -1.5 + -1.066x + 0.55x2 = 1.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -1.066x + 0.55x2 = 0.0 Begin completing the square. Divide all terms by 0.55 the coefficient of the squared term: Divide each side by '0.55'. -2.727272727 + -1.938181818x + x2 = 0 Move the constant term to the right: Add '2.727272727' to each side of the equation. -2.727272727 + -1.938181818x + 2.727272727 + x2 = 0 + 2.727272727 Reorder the terms: -2.727272727 + 2.727272727 + -1.938181818x + x2 = 0 + 2.727272727 Combine like terms: -2.727272727 + 2.727272727 = 0.000000000 0.000000000 + -1.938181818x + x2 = 0 + 2.727272727 -1.938181818x + x2 = 0 + 2.727272727 Combine like terms: 0 + 2.727272727 = 2.727272727 -1.938181818x + x2 = 2.727272727 The x term is -1.938181818x. Take half its coefficient (-0.969090909). Square it (0.9391371899) and add it to both sides. Add '0.9391371899' to each side of the equation. -1.938181818x + 0.9391371899 + x2 = 2.727272727 + 0.9391371899 Reorder the terms: 0.9391371899 + -1.938181818x + x2 = 2.727272727 + 0.9391371899 Combine like terms: 2.727272727 + 0.9391371899 = 3.6664099169 0.9391371899 + -1.938181818x + x2 = 3.6664099169 Factor a perfect square on the left side: (x + -0.969090909)(x + -0.969090909) = 3.6664099169 Calculate the square root of the right side: 1.914787173 Break this problem into two subproblems by setting (x + -0.969090909) equal to 1.914787173 and -1.914787173.Subproblem 1
x + -0.969090909 = 1.914787173 Simplifying x + -0.969090909 = 1.914787173 Reorder the terms: -0.969090909 + x = 1.914787173 Solving -0.969090909 + x = 1.914787173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.969090909' to each side of the equation. -0.969090909 + 0.969090909 + x = 1.914787173 + 0.969090909 Combine like terms: -0.969090909 + 0.969090909 = 0.000000000 0.000000000 + x = 1.914787173 + 0.969090909 x = 1.914787173 + 0.969090909 Combine like terms: 1.914787173 + 0.969090909 = 2.883878082 x = 2.883878082 Simplifying x = 2.883878082Subproblem 2
x + -0.969090909 = -1.914787173 Simplifying x + -0.969090909 = -1.914787173 Reorder the terms: -0.969090909 + x = -1.914787173 Solving -0.969090909 + x = -1.914787173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.969090909' to each side of the equation. -0.969090909 + 0.969090909 + x = -1.914787173 + 0.969090909 Combine like terms: -0.969090909 + 0.969090909 = 0.000000000 0.000000000 + x = -1.914787173 + 0.969090909 x = -1.914787173 + 0.969090909 Combine like terms: -1.914787173 + 0.969090909 = -0.945696264 x = -0.945696264 Simplifying x = -0.945696264Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.883878082, -0.945696264}
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