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Simplifying 3(x + -11) * x + -3 = 11 Reorder the terms: 3(-11 + x) * x + -3 = 11 Reorder the terms for easier multiplication: 3x(-11 + x) + -3 = 11 (-11 * 3x + x * 3x) + -3 = 11 (-33x + 3x2) + -3 = 11 Reorder the terms: -3 + -33x + 3x2 = 11 Solving -3 + -33x + 3x2 = 11 Solving for variable 'x'. Reorder the terms: -3 + -11 + -33x + 3x2 = 11 + -11 Combine like terms: -3 + -11 = -14 -14 + -33x + 3x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -14 + -33x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4.666666667 + -11x + x2 = 0 Move the constant term to the right: Add '4.666666667' to each side of the equation. -4.666666667 + -11x + 4.666666667 + x2 = 0 + 4.666666667 Reorder the terms: -4.666666667 + 4.666666667 + -11x + x2 = 0 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + -11x + x2 = 0 + 4.666666667 -11x + x2 = 0 + 4.666666667 Combine like terms: 0 + 4.666666667 = 4.666666667 -11x + x2 = 4.666666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 4.666666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 4.666666667 + 30.25 Combine like terms: 4.666666667 + 30.25 = 34.916666667 30.25 + -11x + x2 = 34.916666667 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 34.916666667 Calculate the square root of the right side: 5.909032634 Break this problem into two subproblems by setting (x + -5.5) equal to 5.909032634 and -5.909032634.Subproblem 1
x + -5.5 = 5.909032634 Simplifying x + -5.5 = 5.909032634 Reorder the terms: -5.5 + x = 5.909032634 Solving -5.5 + x = 5.909032634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.909032634 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.909032634 + 5.5 x = 5.909032634 + 5.5 Combine like terms: 5.909032634 + 5.5 = 11.409032634 x = 11.409032634 Simplifying x = 11.409032634Subproblem 2
x + -5.5 = -5.909032634 Simplifying x + -5.5 = -5.909032634 Reorder the terms: -5.5 + x = -5.909032634 Solving -5.5 + x = -5.909032634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.909032634 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.909032634 + 5.5 x = -5.909032634 + 5.5 Combine like terms: -5.909032634 + 5.5 = -0.409032634 x = -0.409032634 Simplifying x = -0.409032634Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.409032634, -0.409032634}
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