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Simplifying 0 = -16x2 + 32x + 5 Reorder the terms: 0 = 5 + 32x + -16x2 Solving 0 = 5 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -32x + 16x2 = 5 + 32x + -16x2 + -5 + -32x + 16x2 Reorder the terms: -5 + -32x + 16x2 = 5 + -5 + 32x + -32x + -16x2 + 16x2 Combine like terms: 5 + -5 = 0 -5 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -5 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -5 + -32x + 16x2 = 0 + -16x2 + 16x2 -5 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -5 + -32x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -2x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -2x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -2x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -2x + x2 = 0 + 0.3125 -2x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -2x + x2 = 0.3125 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.3125 + 1 Reorder the terms: 1 + -2x + x2 = 0.3125 + 1 Combine like terms: 0.3125 + 1 = 1.3125 1 + -2x + x2 = 1.3125 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (x + -1) equal to 1.145643924 and -1.145643924.Subproblem 1
x + -1 = 1.145643924 Simplifying x + -1 = 1.145643924 Reorder the terms: -1 + x = 1.145643924 Solving -1 + x = 1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.145643924 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.145643924 + 1 x = 1.145643924 + 1 Combine like terms: 1.145643924 + 1 = 2.145643924 x = 2.145643924 Simplifying x = 2.145643924Subproblem 2
x + -1 = -1.145643924 Simplifying x + -1 = -1.145643924 Reorder the terms: -1 + x = -1.145643924 Solving -1 + x = -1.145643924 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.145643924 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.145643924 + 1 x = -1.145643924 + 1 Combine like terms: -1.145643924 + 1 = -0.145643924 x = -0.145643924 Simplifying x = -0.145643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.145643924, -0.145643924}
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