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Simplifying 0.75x2 + -0.33x + -1 = 0 Reorder the terms: -1 + -0.33x + 0.75x2 = 0 Solving -1 + -0.33x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. -1.333333333 + -0.44x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.44x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.44x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.44x + x2 = 0 + 1.333333333 -0.44x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.44x + x2 = 1.333333333 The x term is -0.44x. Take half its coefficient (-0.22). Square it (0.0484) and add it to both sides. Add '0.0484' to each side of the equation. -0.44x + 0.0484 + x2 = 1.333333333 + 0.0484 Reorder the terms: 0.0484 + -0.44x + x2 = 1.333333333 + 0.0484 Combine like terms: 1.333333333 + 0.0484 = 1.381733333 0.0484 + -0.44x + x2 = 1.381733333 Factor a perfect square on the left side: (x + -0.22)(x + -0.22) = 1.381733333 Calculate the square root of the right side: 1.175471536 Break this problem into two subproblems by setting (x + -0.22) equal to 1.175471536 and -1.175471536.Subproblem 1
x + -0.22 = 1.175471536 Simplifying x + -0.22 = 1.175471536 Reorder the terms: -0.22 + x = 1.175471536 Solving -0.22 + x = 1.175471536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = 1.175471536 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = 1.175471536 + 0.22 x = 1.175471536 + 0.22 Combine like terms: 1.175471536 + 0.22 = 1.395471536 x = 1.395471536 Simplifying x = 1.395471536Subproblem 2
x + -0.22 = -1.175471536 Simplifying x + -0.22 = -1.175471536 Reorder the terms: -0.22 + x = -1.175471536 Solving -0.22 + x = -1.175471536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.22' to each side of the equation. -0.22 + 0.22 + x = -1.175471536 + 0.22 Combine like terms: -0.22 + 0.22 = 0.00 0.00 + x = -1.175471536 + 0.22 x = -1.175471536 + 0.22 Combine like terms: -1.175471536 + 0.22 = -0.955471536 x = -0.955471536 Simplifying x = -0.955471536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.395471536, -0.955471536}
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