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Simplifying 1 = -0.5 * 32x2 + 60x + 6 Multiply -0.5 * 32 1 = -16x2 + 60x + 6 Reorder the terms: 1 = 6 + 60x + -16x2 Solving 1 = 6 + 60x + -16x2 Solving for variable 'x'. Combine like terms: 1 + -6 = -5 -5 + -60x + 16x2 = 6 + 60x + -16x2 + -6 + -60x + 16x2 Reorder the terms: -5 + -60x + 16x2 = 6 + -6 + 60x + -60x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 -5 + -60x + 16x2 = 0 + 60x + -60x + -16x2 + 16x2 -5 + -60x + 16x2 = 60x + -60x + -16x2 + 16x2 Combine like terms: 60x + -60x = 0 -5 + -60x + 16x2 = 0 + -16x2 + 16x2 -5 + -60x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -60x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -3.75x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -3.75x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -3.75x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -3.75x + x2 = 0 + 0.3125 -3.75x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -3.75x + x2 = 0.3125 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 = 0.3125 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 0.3125 + 3.515625 Combine like terms: 0.3125 + 3.515625 = 3.828125 3.515625 + -3.75x + x2 = 3.828125 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 3.828125 Calculate the square root of the right side: 1.95655948 Break this problem into two subproblems by setting (x + -1.875) equal to 1.95655948 and -1.95655948.Subproblem 1
x + -1.875 = 1.95655948 Simplifying x + -1.875 = 1.95655948 Reorder the terms: -1.875 + x = 1.95655948 Solving -1.875 + x = 1.95655948 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 = 1.95655948 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.95655948 + 1.875 x = 1.95655948 + 1.875 Combine like terms: 1.95655948 + 1.875 = 3.83155948 x = 3.83155948 Simplifying x = 3.83155948Subproblem 2
x + -1.875 = -1.95655948 Simplifying x + -1.875 = -1.95655948 Reorder the terms: -1.875 + x = -1.95655948 Solving -1.875 + x = -1.95655948 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 = -1.95655948 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.95655948 + 1.875 x = -1.95655948 + 1.875 Combine like terms: -1.95655948 + 1.875 = -0.08155948 x = -0.08155948 Simplifying x = -0.08155948Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.83155948, -0.08155948}
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