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Simplifying (-4x2 + -3x + 6) + (-9x2 + -1) = 0 Reorder the terms: (6 + -3x + -4x2) + (-9x2 + -1) = 0 Remove parenthesis around (6 + -3x + -4x2) 6 + -3x + -4x2 + (-9x2 + -1) = 0 Reorder the terms: 6 + -3x + -4x2 + (-1 + -9x2) = 0 Remove parenthesis around (-1 + -9x2) 6 + -3x + -4x2 + -1 + -9x2 = 0 Reorder the terms: 6 + -1 + -3x + -4x2 + -9x2 = 0 Combine like terms: 6 + -1 = 5 5 + -3x + -4x2 + -9x2 = 0 Combine like terms: -4x2 + -9x2 = -13x2 5 + -3x + -13x2 = 0 Solving 5 + -3x + -13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -0.3846153846 + 0.2307692308x + x2 = 0 Move the constant term to the right: Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.2307692308x + 0.3846153846 + x2 = 0 + 0.3846153846 Reorder the terms: -0.3846153846 + 0.3846153846 + 0.2307692308x + x2 = 0 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + 0.2307692308x + x2 = 0 + 0.3846153846 0.2307692308x + x2 = 0 + 0.3846153846 Combine like terms: 0 + 0.3846153846 = 0.3846153846 0.2307692308x + x2 = 0.3846153846 The x term is 0.2307692308x. Take half its coefficient (0.1153846154). Square it (0.01331360947) and add it to both sides. Add '0.01331360947' to each side of the equation. 0.2307692308x + 0.01331360947 + x2 = 0.3846153846 + 0.01331360947 Reorder the terms: 0.01331360947 + 0.2307692308x + x2 = 0.3846153846 + 0.01331360947 Combine like terms: 0.3846153846 + 0.01331360947 = 0.39792899407 0.01331360947 + 0.2307692308x + x2 = 0.39792899407 Factor a perfect square on the left side: (x + 0.1153846154)(x + 0.1153846154) = 0.39792899407 Calculate the square root of the right side: 0.630816133 Break this problem into two subproblems by setting (x + 0.1153846154) equal to 0.630816133 and -0.630816133.Subproblem 1
x + 0.1153846154 = 0.630816133 Simplifying x + 0.1153846154 = 0.630816133 Reorder the terms: 0.1153846154 + x = 0.630816133 Solving 0.1153846154 + x = 0.630816133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = 0.630816133 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = 0.630816133 + -0.1153846154 x = 0.630816133 + -0.1153846154 Combine like terms: 0.630816133 + -0.1153846154 = 0.5154315176 x = 0.5154315176 Simplifying x = 0.5154315176Subproblem 2
x + 0.1153846154 = -0.630816133 Simplifying x + 0.1153846154 = -0.630816133 Reorder the terms: 0.1153846154 + x = -0.630816133 Solving 0.1153846154 + x = -0.630816133 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1153846154' to each side of the equation. 0.1153846154 + -0.1153846154 + x = -0.630816133 + -0.1153846154 Combine like terms: 0.1153846154 + -0.1153846154 = 0.0000000000 0.0000000000 + x = -0.630816133 + -0.1153846154 x = -0.630816133 + -0.1153846154 Combine like terms: -0.630816133 + -0.1153846154 = -0.7462007484 x = -0.7462007484 Simplifying x = -0.7462007484Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5154315176, -0.7462007484}
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