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Simplifying -16x2 + 55x + 138 = 0 Reorder the terms: 138 + 55x + -16x2 = 0 Solving 138 + 55x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -8.625 + -3.4375x + x2 = 0 Move the constant term to the right: Add '8.625' to each side of the equation. -8.625 + -3.4375x + 8.625 + x2 = 0 + 8.625 Reorder the terms: -8.625 + 8.625 + -3.4375x + x2 = 0 + 8.625 Combine like terms: -8.625 + 8.625 = 0.000 0.000 + -3.4375x + x2 = 0 + 8.625 -3.4375x + x2 = 0 + 8.625 Combine like terms: 0 + 8.625 = 8.625 -3.4375x + x2 = 8.625 The x term is -3.4375x. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375x + 2.954101563 + x2 = 8.625 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375x + x2 = 8.625 + 2.954101563 Combine like terms: 8.625 + 2.954101563 = 11.579101563 2.954101563 + -3.4375x + x2 = 11.579101563 Factor a perfect square on the left side: (x + -1.71875)(x + -1.71875) = 11.579101563 Calculate the square root of the right side: 3.402807894 Break this problem into two subproblems by setting (x + -1.71875) equal to 3.402807894 and -3.402807894.Subproblem 1
x + -1.71875 = 3.402807894 Simplifying x + -1.71875 = 3.402807894 Reorder the terms: -1.71875 + x = 3.402807894 Solving -1.71875 + x = 3.402807894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = 3.402807894 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = 3.402807894 + 1.71875 x = 3.402807894 + 1.71875 Combine like terms: 3.402807894 + 1.71875 = 5.121557894 x = 5.121557894 Simplifying x = 5.121557894Subproblem 2
x + -1.71875 = -3.402807894 Simplifying x + -1.71875 = -3.402807894 Reorder the terms: -1.71875 + x = -3.402807894 Solving -1.71875 + x = -3.402807894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = -3.402807894 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = -3.402807894 + 1.71875 x = -3.402807894 + 1.71875 Combine like terms: -3.402807894 + 1.71875 = -1.684057894 x = -1.684057894 Simplifying x = -1.684057894Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.121557894, -1.684057894}
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