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Simplifying -16x2 + 60x + 5 = 50 Reorder the terms: 5 + 60x + -16x2 = 50 Solving 5 + 60x + -16x2 = 50 Solving for variable 'x'. Reorder the terms: 5 + -50 + 60x + -16x2 = 50 + -50 Combine like terms: 5 + -50 = -45 -45 + 60x + -16x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -45 + 60x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.8125 + -3.75x + x2 = 0 Move the constant term to the right: Add '-2.8125' to each side of the equation. 2.8125 + -3.75x + -2.8125 + x2 = 0 + -2.8125 Reorder the terms: 2.8125 + -2.8125 + -3.75x + x2 = 0 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + -3.75x + x2 = 0 + -2.8125 -3.75x + x2 = 0 + -2.8125 Combine like terms: 0 + -2.8125 = -2.8125 -3.75x + x2 = -2.8125 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = -2.8125 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = -2.8125 + 3.515625 Combine like terms: -2.8125 + 3.515625 = 0.703125 3.515625 + -3.75x + x2 = 0.703125 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 0.703125 Calculate the square root of the right side: 0.838525492 Break this problem into two subproblems by setting (x + -1.875) equal to 0.838525492 and -0.838525492.Subproblem 1
x + -1.875 = 0.838525492 Simplifying x + -1.875 = 0.838525492 Reorder the terms: -1.875 + x = 0.838525492 Solving -1.875 + x = 0.838525492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 0.838525492 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 0.838525492 + 1.875 x = 0.838525492 + 1.875 Combine like terms: 0.838525492 + 1.875 = 2.713525492 x = 2.713525492 Simplifying x = 2.713525492Subproblem 2
x + -1.875 = -0.838525492 Simplifying x + -1.875 = -0.838525492 Reorder the terms: -1.875 + x = -0.838525492 Solving -1.875 + x = -0.838525492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -0.838525492 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -0.838525492 + 1.875 x = -0.838525492 + 1.875 Combine like terms: -0.838525492 + 1.875 = 1.036474508 x = 1.036474508 Simplifying x = 1.036474508Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.713525492, 1.036474508}
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