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Simplifying -16x2 + -32x + 5 = 0 Reorder the terms: 5 + -32x + -16x2 = 0 Solving 5 + -32x + -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'. -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 = 0.145643924 x = 0.145643924 Simplifying x = 0.145643924Subproblem 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 = -2.145643924 x = -2.145643924 Simplifying x = -2.145643924Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.145643924, -2.145643924}
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