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Simplifying 0 = -16x2 + 32x + 64 Reorder the terms: 0 = 64 + 32x + -16x2 Solving 0 = 64 + 32x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -64 = -64 -64 + -32x + 16x2 = 64 + 32x + -16x2 + -64 + -32x + 16x2 Reorder the terms: -64 + -32x + 16x2 = 64 + -64 + 32x + -32x + -16x2 + 16x2 Combine like terms: 64 + -64 = 0 -64 + -32x + 16x2 = 0 + 32x + -32x + -16x2 + 16x2 -64 + -32x + 16x2 = 32x + -32x + -16x2 + 16x2 Combine like terms: 32x + -32x = 0 -64 + -32x + 16x2 = 0 + -16x2 + 16x2 -64 + -32x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -64 + -32x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-4 + -2x + x2) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-4 + -2x + x2)' equal to zero and attempt to solve: Simplifying -4 + -2x + x2 = 0 Solving -4 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -2x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -2x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -2x + x2 = 0 + 4 -2x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -2x + x2 = 4 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 = 4 + 1 Reorder the terms: 1 + -2x + x2 = 4 + 1 Combine like terms: 4 + 1 = 5 1 + -2x + x2 = 5 Factor a perfect square on the left side: (x + -1)(x + -1) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -1) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -1 = 2.236067978 Simplifying x + -1 = 2.236067978 Reorder the terms: -1 + x = 2.236067978 Solving -1 + x = 2.236067978 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 = 2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.236067978 + 1 x = 2.236067978 + 1 Combine like terms: 2.236067978 + 1 = 3.236067978 x = 3.236067978 Simplifying x = 3.236067978Subproblem 2
x + -1 = -2.236067978 Simplifying x + -1 = -2.236067978 Reorder the terms: -1 + x = -2.236067978 Solving -1 + x = -2.236067978 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 = -2.236067978 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.236067978 + 1 x = -2.236067978 + 1 Combine like terms: -2.236067978 + 1 = -1.236067978 x = -1.236067978 Simplifying x = -1.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.236067978, -1.236067978}Solution
x = {3.236067978, -1.236067978}
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