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Simplifying -16x2 + 75x + 3 = 25 Reorder the terms: 3 + 75x + -16x2 = 25 Solving 3 + 75x + -16x2 = 25 Solving for variable 'x'. Reorder the terms: 3 + -25 + 75x + -16x2 = 25 + -25 Combine like terms: 3 + -25 = -22 -22 + 75x + -16x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -22 + 75x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.375 + -4.6875x + x2 = 0 Move the constant term to the right: Add '-1.375' to each side of the equation. 1.375 + -4.6875x + -1.375 + x2 = 0 + -1.375 Reorder the terms: 1.375 + -1.375 + -4.6875x + x2 = 0 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + -4.6875x + x2 = 0 + -1.375 -4.6875x + x2 = 0 + -1.375 Combine like terms: 0 + -1.375 = -1.375 -4.6875x + x2 = -1.375 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 = -1.375 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875x + x2 = -1.375 + 5.493164063 Combine like terms: -1.375 + 5.493164063 = 4.118164063 5.493164063 + -4.6875x + x2 = 4.118164063 Factor a perfect square on the left side: (x + -2.34375)(x + -2.34375) = 4.118164063 Calculate the square root of the right side: 2.029326012 Break this problem into two subproblems by setting (x + -2.34375) equal to 2.029326012 and -2.029326012.Subproblem 1
x + -2.34375 = 2.029326012 Simplifying x + -2.34375 = 2.029326012 Reorder the terms: -2.34375 + x = 2.029326012 Solving -2.34375 + x = 2.029326012 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 = 2.029326012 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = 2.029326012 + 2.34375 x = 2.029326012 + 2.34375 Combine like terms: 2.029326012 + 2.34375 = 4.373076012 x = 4.373076012 Simplifying x = 4.373076012Subproblem 2
x + -2.34375 = -2.029326012 Simplifying x + -2.34375 = -2.029326012 Reorder the terms: -2.34375 + x = -2.029326012 Solving -2.34375 + x = -2.029326012 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 = -2.029326012 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + x = -2.029326012 + 2.34375 x = -2.029326012 + 2.34375 Combine like terms: -2.029326012 + 2.34375 = 0.314423988 x = 0.314423988 Simplifying x = 0.314423988Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.373076012, 0.314423988}
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