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Simplifying 185 = -16x2 + 103x + 40 Reorder the terms: 185 = 40 + 103x + -16x2 Solving 185 = 40 + 103x + -16x2 Solving for variable 'x'. Combine like terms: 185 + -40 = 145 145 + -103x + 16x2 = 40 + 103x + -16x2 + -40 + -103x + 16x2 Reorder the terms: 145 + -103x + 16x2 = 40 + -40 + 103x + -103x + -16x2 + 16x2 Combine like terms: 40 + -40 = 0 145 + -103x + 16x2 = 0 + 103x + -103x + -16x2 + 16x2 145 + -103x + 16x2 = 103x + -103x + -16x2 + 16x2 Combine like terms: 103x + -103x = 0 145 + -103x + 16x2 = 0 + -16x2 + 16x2 145 + -103x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 145 + -103x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 9.0625 + -6.4375x + x2 = 0 Move the constant term to the right: Add '-9.0625' to each side of the equation. 9.0625 + -6.4375x + -9.0625 + x2 = 0 + -9.0625 Reorder the terms: 9.0625 + -9.0625 + -6.4375x + x2 = 0 + -9.0625 Combine like terms: 9.0625 + -9.0625 = 0.0000 0.0000 + -6.4375x + x2 = 0 + -9.0625 -6.4375x + x2 = 0 + -9.0625 Combine like terms: 0 + -9.0625 = -9.0625 -6.4375x + x2 = -9.0625 The x term is -6.4375x. Take half its coefficient (-3.21875). Square it (10.36035156) and add it to both sides. Add '10.36035156' to each side of the equation. -6.4375x + 10.36035156 + x2 = -9.0625 + 10.36035156 Reorder the terms: 10.36035156 + -6.4375x + x2 = -9.0625 + 10.36035156 Combine like terms: -9.0625 + 10.36035156 = 1.29785156 10.36035156 + -6.4375x + x2 = 1.29785156 Factor a perfect square on the left side: (x + -3.21875)(x + -3.21875) = 1.29785156 Calculate the square root of the right side: 1.139232882 Break this problem into two subproblems by setting (x + -3.21875) equal to 1.139232882 and -1.139232882.Subproblem 1
x + -3.21875 = 1.139232882 Simplifying x + -3.21875 = 1.139232882 Reorder the terms: -3.21875 + x = 1.139232882 Solving -3.21875 + x = 1.139232882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.21875' to each side of the equation. -3.21875 + 3.21875 + x = 1.139232882 + 3.21875 Combine like terms: -3.21875 + 3.21875 = 0.00000 0.00000 + x = 1.139232882 + 3.21875 x = 1.139232882 + 3.21875 Combine like terms: 1.139232882 + 3.21875 = 4.357982882 x = 4.357982882 Simplifying x = 4.357982882Subproblem 2
x + -3.21875 = -1.139232882 Simplifying x + -3.21875 = -1.139232882 Reorder the terms: -3.21875 + x = -1.139232882 Solving -3.21875 + x = -1.139232882 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.21875' to each side of the equation. -3.21875 + 3.21875 + x = -1.139232882 + 3.21875 Combine like terms: -3.21875 + 3.21875 = 0.00000 0.00000 + x = -1.139232882 + 3.21875 x = -1.139232882 + 3.21875 Combine like terms: -1.139232882 + 3.21875 = 2.079517118 x = 2.079517118 Simplifying x = 2.079517118Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.357982882, 2.079517118}
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