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Simplifying -16x2 + 60x + 35 = 0 Reorder the terms: 35 + 60x + -16x2 = 0 Solving 35 + 60x + -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'. -2.1875 + -3.75x + x2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + -3.75x + 2.1875 + x2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + -3.75x + x2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + -3.75x + x2 = 0 + 2.1875 -3.75x + x2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 -3.75x + x2 = 2.1875 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 = 2.1875 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 2.1875 + 3.515625 Combine like terms: 2.1875 + 3.515625 = 5.703125 3.515625 + -3.75x + x2 = 5.703125 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 5.703125 Calculate the square root of the right side: 2.388121647 Break this problem into two subproblems by setting (x + -1.875) equal to 2.388121647 and -2.388121647.Subproblem 1
x + -1.875 = 2.388121647 Simplifying x + -1.875 = 2.388121647 Reorder the terms: -1.875 + x = 2.388121647 Solving -1.875 + x = 2.388121647 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 = 2.388121647 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 2.388121647 + 1.875 x = 2.388121647 + 1.875 Combine like terms: 2.388121647 + 1.875 = 4.263121647 x = 4.263121647 Simplifying x = 4.263121647Subproblem 2
x + -1.875 = -2.388121647 Simplifying x + -1.875 = -2.388121647 Reorder the terms: -1.875 + x = -2.388121647 Solving -1.875 + x = -2.388121647 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 = -2.388121647 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -2.388121647 + 1.875 x = -2.388121647 + 1.875 Combine like terms: -2.388121647 + 1.875 = -0.513121647 x = -0.513121647 Simplifying x = -0.513121647Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.263121647, -0.513121647}
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