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Simplifying 663.74 = 84.45x + 13.3x2 Solving 663.74 = 84.45x + 13.3x2 Solving for variable 'x'. Reorder the terms: 663.74 + -84.45x + -13.3x2 = 84.45x + -84.45x + 13.3x2 + -13.3x2 Combine like terms: 84.45x + -84.45x = 0.00 663.74 + -84.45x + -13.3x2 = 0.00 + 13.3x2 + -13.3x2 663.74 + -84.45x + -13.3x2 = 13.3x2 + -13.3x2 Combine like terms: 13.3x2 + -13.3x2 = 0.0 663.74 + -84.45x + -13.3x2 = 0.0 Begin completing the square. Divide all terms by -13.3 the coefficient of the squared term: Divide each side by '-13.3'. -49.90526316 + 6.34962406x + x2 = 0 Move the constant term to the right: Add '49.90526316' to each side of the equation. -49.90526316 + 6.34962406x + 49.90526316 + x2 = 0 + 49.90526316 Reorder the terms: -49.90526316 + 49.90526316 + 6.34962406x + x2 = 0 + 49.90526316 Combine like terms: -49.90526316 + 49.90526316 = 0.00000000 0.00000000 + 6.34962406x + x2 = 0 + 49.90526316 6.34962406x + x2 = 0 + 49.90526316 Combine like terms: 0 + 49.90526316 = 49.90526316 6.34962406x + x2 = 49.90526316 The x term is 6.34962406x. Take half its coefficient (3.17481203). Square it (10.07943143) and add it to both sides. Add '10.07943143' to each side of the equation. 6.34962406x + 10.07943143 + x2 = 49.90526316 + 10.07943143 Reorder the terms: 10.07943143 + 6.34962406x + x2 = 49.90526316 + 10.07943143 Combine like terms: 49.90526316 + 10.07943143 = 59.98469459 10.07943143 + 6.34962406x + x2 = 59.98469459 Factor a perfect square on the left side: (x + 3.17481203)(x + 3.17481203) = 59.98469459 Calculate the square root of the right side: 7.744978669 Break this problem into two subproblems by setting (x + 3.17481203) equal to 7.744978669 and -7.744978669.Subproblem 1
x + 3.17481203 = 7.744978669 Simplifying x + 3.17481203 = 7.744978669 Reorder the terms: 3.17481203 + x = 7.744978669 Solving 3.17481203 + x = 7.744978669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.17481203' to each side of the equation. 3.17481203 + -3.17481203 + x = 7.744978669 + -3.17481203 Combine like terms: 3.17481203 + -3.17481203 = 0.00000000 0.00000000 + x = 7.744978669 + -3.17481203 x = 7.744978669 + -3.17481203 Combine like terms: 7.744978669 + -3.17481203 = 4.570166639 x = 4.570166639 Simplifying x = 4.570166639Subproblem 2
x + 3.17481203 = -7.744978669 Simplifying x + 3.17481203 = -7.744978669 Reorder the terms: 3.17481203 + x = -7.744978669 Solving 3.17481203 + x = -7.744978669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.17481203' to each side of the equation. 3.17481203 + -3.17481203 + x = -7.744978669 + -3.17481203 Combine like terms: 3.17481203 + -3.17481203 = 0.00000000 0.00000000 + x = -7.744978669 + -3.17481203 x = -7.744978669 + -3.17481203 Combine like terms: -7.744978669 + -3.17481203 = -10.919790699 x = -10.919790699 Simplifying x = -10.919790699Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.570166639, -10.919790699}
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