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Simplifying 2(3x + -4) + (-1x2 + 5x + -3) = 0 Reorder the terms: 2(-4 + 3x) + (-1x2 + 5x + -3) = 0 (-4 * 2 + 3x * 2) + (-1x2 + 5x + -3) = 0 (-8 + 6x) + (-1x2 + 5x + -3) = 0 Reorder the terms: -8 + 6x + (-3 + 5x + -1x2) = 0 Remove parenthesis around (-3 + 5x + -1x2) -8 + 6x + -3 + 5x + -1x2 = 0 Reorder the terms: -8 + -3 + 6x + 5x + -1x2 = 0 Combine like terms: -8 + -3 = -11 -11 + 6x + 5x + -1x2 = 0 Combine like terms: 6x + 5x = 11x -11 + 11x + -1x2 = 0 Solving -11 + 11x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -11x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -11x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -11x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -11x + x2 = 0 + -11 -11x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -11x + x2 = -11 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 = -11 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -11 + 30.25 Combine like terms: -11 + 30.25 = 19.25 30.25 + -11x + x2 = 19.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (x + -5.5) equal to 4.387482194 and -4.387482194.Subproblem 1
x + -5.5 = 4.387482194 Simplifying x + -5.5 = 4.387482194 Reorder the terms: -5.5 + x = 4.387482194 Solving -5.5 + x = 4.387482194 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 = 4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.387482194 + 5.5 x = 4.387482194 + 5.5 Combine like terms: 4.387482194 + 5.5 = 9.887482194 x = 9.887482194 Simplifying x = 9.887482194Subproblem 2
x + -5.5 = -4.387482194 Simplifying x + -5.5 = -4.387482194 Reorder the terms: -5.5 + x = -4.387482194 Solving -5.5 + x = -4.387482194 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 = -4.387482194 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.387482194 + 5.5 x = -4.387482194 + 5.5 Combine like terms: -4.387482194 + 5.5 = 1.112517806 x = 1.112517806 Simplifying x = 1.112517806Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.887482194, 1.112517806}
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