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Simplifying 23x + 55(x2) = 1192 Solving 23x + 55x2 = 1192 Solving for variable 'x'. Reorder the terms: -1192 + 23x + 55x2 = 1192 + -1192 Combine like terms: 1192 + -1192 = 0 -1192 + 23x + 55x2 = 0 Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. -21.67272727 + 0.4181818182x + x2 = 0 Move the constant term to the right: Add '21.67272727' to each side of the equation. -21.67272727 + 0.4181818182x + 21.67272727 + x2 = 0 + 21.67272727 Reorder the terms: -21.67272727 + 21.67272727 + 0.4181818182x + x2 = 0 + 21.67272727 Combine like terms: -21.67272727 + 21.67272727 = 0.00000000 0.00000000 + 0.4181818182x + x2 = 0 + 21.67272727 0.4181818182x + x2 = 0 + 21.67272727 Combine like terms: 0 + 21.67272727 = 21.67272727 0.4181818182x + x2 = 21.67272727 The x term is 0.4181818182x. Take half its coefficient (0.2090909091). Square it (0.04371900827) and add it to both sides. Add '0.04371900827' to each side of the equation. 0.4181818182x + 0.04371900827 + x2 = 21.67272727 + 0.04371900827 Reorder the terms: 0.04371900827 + 0.4181818182x + x2 = 21.67272727 + 0.04371900827 Combine like terms: 21.67272727 + 0.04371900827 = 21.71644627827 0.04371900827 + 0.4181818182x + x2 = 21.71644627827 Factor a perfect square on the left side: (x + 0.2090909091)(x + 0.2090909091) = 21.71644627827 Calculate the square root of the right side: 4.660090802 Break this problem into two subproblems by setting (x + 0.2090909091) equal to 4.660090802 and -4.660090802.Subproblem 1
x + 0.2090909091 = 4.660090802 Simplifying x + 0.2090909091 = 4.660090802 Reorder the terms: 0.2090909091 + x = 4.660090802 Solving 0.2090909091 + x = 4.660090802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2090909091' to each side of the equation. 0.2090909091 + -0.2090909091 + x = 4.660090802 + -0.2090909091 Combine like terms: 0.2090909091 + -0.2090909091 = 0.0000000000 0.0000000000 + x = 4.660090802 + -0.2090909091 x = 4.660090802 + -0.2090909091 Combine like terms: 4.660090802 + -0.2090909091 = 4.4509998929 x = 4.4509998929 Simplifying x = 4.4509998929Subproblem 2
x + 0.2090909091 = -4.660090802 Simplifying x + 0.2090909091 = -4.660090802 Reorder the terms: 0.2090909091 + x = -4.660090802 Solving 0.2090909091 + x = -4.660090802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2090909091' to each side of the equation. 0.2090909091 + -0.2090909091 + x = -4.660090802 + -0.2090909091 Combine like terms: 0.2090909091 + -0.2090909091 = 0.0000000000 0.0000000000 + x = -4.660090802 + -0.2090909091 x = -4.660090802 + -0.2090909091 Combine like terms: -4.660090802 + -0.2090909091 = -4.8691817111 x = -4.8691817111 Simplifying x = -4.8691817111Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4509998929, -4.8691817111}
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