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Simplifying 4x2 + -11x + -16 = 0 Reorder the terms: -16 + -11x + 4x2 = 0 Solving -16 + -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'. -4 + -2.75x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -2.75x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2.75x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2.75x + x2 = 0 + 4 -2.75x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2.75x + x2 = 4 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 = 4 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 4 + 1.890625 Combine like terms: 4 + 1.890625 = 5.890625 1.890625 + -2.75x + x2 = 5.890625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -1.375) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -1.375 = 2.42706098 Simplifying x + -1.375 = 2.42706098 Reorder the terms: -1.375 + x = 2.42706098 Solving -1.375 + x = 2.42706098 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 = 2.42706098 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.42706098 + 1.375 x = 2.42706098 + 1.375 Combine like terms: 2.42706098 + 1.375 = 3.80206098 x = 3.80206098 Simplifying x = 3.80206098Subproblem 2
x + -1.375 = -2.42706098 Simplifying x + -1.375 = -2.42706098 Reorder the terms: -1.375 + x = -2.42706098 Solving -1.375 + x = -2.42706098 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 = -2.42706098 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.42706098 + 1.375 x = -2.42706098 + 1.375 Combine like terms: -2.42706098 + 1.375 = -1.05206098 x = -1.05206098 Simplifying x = -1.05206098Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.80206098, -1.05206098}
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