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Simplifying (8x2 + 3x + 1) + (9x2 + 8x) = 0 Reorder the terms: (1 + 3x + 8x2) + (9x2 + 8x) = 0 Remove parenthesis around (1 + 3x + 8x2) 1 + 3x + 8x2 + (9x2 + 8x) = 0 Reorder the terms: 1 + 3x + 8x2 + (8x + 9x2) = 0 Remove parenthesis around (8x + 9x2) 1 + 3x + 8x2 + 8x + 9x2 = 0 Reorder the terms: 1 + 3x + 8x + 8x2 + 9x2 = 0 Combine like terms: 3x + 8x = 11x 1 + 11x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 1 + 11x + 17x2 = 0 Solving 1 + 11x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 0.05882352941 + 0.6470588235x + x2 = 0 Move the constant term to the right: Add '-0.05882352941' to each side of the equation. 0.05882352941 + 0.6470588235x + -0.05882352941 + x2 = 0 + -0.05882352941 Reorder the terms: 0.05882352941 + -0.05882352941 + 0.6470588235x + x2 = 0 + -0.05882352941 Combine like terms: 0.05882352941 + -0.05882352941 = 0.00000000000 0.00000000000 + 0.6470588235x + x2 = 0 + -0.05882352941 0.6470588235x + x2 = 0 + -0.05882352941 Combine like terms: 0 + -0.05882352941 = -0.05882352941 0.6470588235x + x2 = -0.05882352941 The x term is 0.6470588235x. Take half its coefficient (0.3235294118). Square it (0.1046712803) and add it to both sides. Add '0.1046712803' to each side of the equation. 0.6470588235x + 0.1046712803 + x2 = -0.05882352941 + 0.1046712803 Reorder the terms: 0.1046712803 + 0.6470588235x + x2 = -0.05882352941 + 0.1046712803 Combine like terms: -0.05882352941 + 0.1046712803 = 0.04584775089 0.1046712803 + 0.6470588235x + x2 = 0.04584775089 Factor a perfect square on the left side: (x + 0.3235294118)(x + 0.3235294118) = 0.04584775089 Calculate the square root of the right side: 0.214120879 Break this problem into two subproblems by setting (x + 0.3235294118) equal to 0.214120879 and -0.214120879.Subproblem 1
x + 0.3235294118 = 0.214120879 Simplifying x + 0.3235294118 = 0.214120879 Reorder the terms: 0.3235294118 + x = 0.214120879 Solving 0.3235294118 + x = 0.214120879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3235294118' to each side of the equation. 0.3235294118 + -0.3235294118 + x = 0.214120879 + -0.3235294118 Combine like terms: 0.3235294118 + -0.3235294118 = 0.0000000000 0.0000000000 + x = 0.214120879 + -0.3235294118 x = 0.214120879 + -0.3235294118 Combine like terms: 0.214120879 + -0.3235294118 = -0.1094085328 x = -0.1094085328 Simplifying x = -0.1094085328Subproblem 2
x + 0.3235294118 = -0.214120879 Simplifying x + 0.3235294118 = -0.214120879 Reorder the terms: 0.3235294118 + x = -0.214120879 Solving 0.3235294118 + x = -0.214120879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3235294118' to each side of the equation. 0.3235294118 + -0.3235294118 + x = -0.214120879 + -0.3235294118 Combine like terms: 0.3235294118 + -0.3235294118 = 0.0000000000 0.0000000000 + x = -0.214120879 + -0.3235294118 x = -0.214120879 + -0.3235294118 Combine like terms: -0.214120879 + -0.3235294118 = -0.5376502908 x = -0.5376502908 Simplifying x = -0.5376502908Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1094085328, -0.5376502908}
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