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Simplifying 16x2 + -75x + -116 = 0 Reorder the terms: -116 + -75x + 16x2 = 0 Solving -116 + -75x + 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'. -7.25 + -4.6875x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -4.6875x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -4.6875x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -4.6875x + x2 = 0 + 7.25 -4.6875x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -4.6875x + x2 = 7.25 The x term is -4.6875x. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875x + 5.493164063 + x2 = 7.25 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875x + x2 = 7.25 + 5.493164063 Combine like terms: 7.25 + 5.493164063 = 12.743164063 5.493164063 + -4.6875x + x2 = 12.743164063 Factor a perfect square on the left side: (x + -2.34375)(x + -2.34375) = 12.743164063 Calculate the square root of the right side: 3.569756863 Break this problem into two subproblems by setting (x + -2.34375) equal to 3.569756863 and -3.569756863.Subproblem 1
x + -2.34375 = 3.569756863 Simplifying x + -2.34375 = 3.569756863 Reorder the terms: -2.34375 + x = 3.569756863 Solving -2.34375 + x = 3.569756863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = 3.569756863 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = 3.569756863 + 2.34375 x = 3.569756863 + 2.34375 Combine like terms: 3.569756863 + 2.34375 = 5.913506863 x = 5.913506863 Simplifying x = 5.913506863Subproblem 2
x + -2.34375 = -3.569756863 Simplifying x + -2.34375 = -3.569756863 Reorder the terms: -2.34375 + x = -3.569756863 Solving -2.34375 + x = -3.569756863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + x = -3.569756863 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = -3.569756863 + 2.34375 x = -3.569756863 + 2.34375 Combine like terms: -3.569756863 + 2.34375 = -1.226006863 x = -1.226006863 Simplifying x = -1.226006863Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.913506863, -1.226006863}
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