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Simplifying 3x + -4x2 + 2x + -7x2 + 8 = 0 Reorder the terms: 8 + 3x + 2x + -4x2 + -7x2 = 0 Combine like terms: 3x + 2x = 5x 8 + 5x + -4x2 + -7x2 = 0 Combine like terms: -4x2 + -7x2 = -11x2 8 + 5x + -11x2 = 0 Solving 8 + 5x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.7272727273 + -0.4545454545x + x2 = 0 Move the constant term to the right: Add '0.7272727273' to each side of the equation. -0.7272727273 + -0.4545454545x + 0.7272727273 + x2 = 0 + 0.7272727273 Reorder the terms: -0.7272727273 + 0.7272727273 + -0.4545454545x + x2 = 0 + 0.7272727273 Combine like terms: -0.7272727273 + 0.7272727273 = 0.0000000000 0.0000000000 + -0.4545454545x + x2 = 0 + 0.7272727273 -0.4545454545x + x2 = 0 + 0.7272727273 Combine like terms: 0 + 0.7272727273 = 0.7272727273 -0.4545454545x + x2 = 0.7272727273 The x term is -0.4545454545x. Take half its coefficient (-0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. -0.4545454545x + 0.05165289257 + x2 = 0.7272727273 + 0.05165289257 Reorder the terms: 0.05165289257 + -0.4545454545x + x2 = 0.7272727273 + 0.05165289257 Combine like terms: 0.7272727273 + 0.05165289257 = 0.77892561987 0.05165289257 + -0.4545454545x + x2 = 0.77892561987 Factor a perfect square on the left side: (x + -0.2272727273)(x + -0.2272727273) = 0.77892561987 Calculate the square root of the right side: 0.882567629 Break this problem into two subproblems by setting (x + -0.2272727273) equal to 0.882567629 and -0.882567629.Subproblem 1
x + -0.2272727273 = 0.882567629 Simplifying x + -0.2272727273 = 0.882567629 Reorder the terms: -0.2272727273 + x = 0.882567629 Solving -0.2272727273 + x = 0.882567629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = 0.882567629 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = 0.882567629 + 0.2272727273 x = 0.882567629 + 0.2272727273 Combine like terms: 0.882567629 + 0.2272727273 = 1.1098403563 x = 1.1098403563 Simplifying x = 1.1098403563Subproblem 2
x + -0.2272727273 = -0.882567629 Simplifying x + -0.2272727273 = -0.882567629 Reorder the terms: -0.2272727273 + x = -0.882567629 Solving -0.2272727273 + x = -0.882567629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2272727273' to each side of the equation. -0.2272727273 + 0.2272727273 + x = -0.882567629 + 0.2272727273 Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000 0.0000000000 + x = -0.882567629 + 0.2272727273 x = -0.882567629 + 0.2272727273 Combine like terms: -0.882567629 + 0.2272727273 = -0.6552949017 x = -0.6552949017 Simplifying x = -0.6552949017Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1098403563, -0.6552949017}
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