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Simplifying 5x + 16 + -4x2 + 6x + -5 = 0 Reorder the terms: 16 + -5 + 5x + 6x + -4x2 = 0 Combine like terms: 16 + -5 = 11 11 + 5x + 6x + -4x2 = 0 Combine like terms: 5x + 6x = 11x 11 + 11x + -4x2 = 0 Solving 11 + 11x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + -2.75x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -2.75x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -2.75x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -2.75x + x2 = 0 + 2.75 -2.75x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -2.75x + x2 = 2.75 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 2.75 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 2.75 + 1.890625 Combine like terms: 2.75 + 1.890625 = 4.640625 1.890625 + -2.75x + x2 = 4.640625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (x + -1.375) equal to 2.154210992 and -2.154210992.Subproblem 1
x + -1.375 = 2.154210992 Simplifying x + -1.375 = 2.154210992 Reorder the terms: -1.375 + x = 2.154210992 Solving -1.375 + x = 2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.154210992 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.154210992 + 1.375 x = 2.154210992 + 1.375 Combine like terms: 2.154210992 + 1.375 = 3.529210992 x = 3.529210992 Simplifying x = 3.529210992Subproblem 2
x + -1.375 = -2.154210992 Simplifying x + -1.375 = -2.154210992 Reorder the terms: -1.375 + x = -2.154210992 Solving -1.375 + x = -2.154210992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.154210992 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.154210992 + 1.375 x = -2.154210992 + 1.375 Combine like terms: -2.154210992 + 1.375 = -0.779210992 x = -0.779210992 Simplifying x = -0.779210992Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.529210992, -0.779210992}
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