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Simplifying 0 = 4x2 + 32x + 44 Reorder the terms: 0 = 44 + 32x + 4x2 Solving 0 = 44 + 32x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -44 = -44 -44 + -32x + -4x2 = 44 + 32x + 4x2 + -44 + -32x + -4x2 Reorder the terms: -44 + -32x + -4x2 = 44 + -44 + 32x + -32x + 4x2 + -4x2 Combine like terms: 44 + -44 = 0 -44 + -32x + -4x2 = 0 + 32x + -32x + 4x2 + -4x2 -44 + -32x + -4x2 = 32x + -32x + 4x2 + -4x2 Combine like terms: 32x + -32x = 0 -44 + -32x + -4x2 = 0 + 4x2 + -4x2 -44 + -32x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -44 + -32x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(11 + 8x + x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(11 + 8x + x2)' equal to zero and attempt to solve: Simplifying 11 + 8x + x2 = 0 Solving 11 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 8x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 8x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8x + x2 = 0 + -11 8x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 8x + x2 = -11 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -11 + 16 Reorder the terms: 16 + 8x + x2 = -11 + 16 Combine like terms: -11 + 16 = 5 16 + 8x + x2 = 5 Factor a perfect square on the left side: (x + 4)(x + 4) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + 4) equal to 2.236067978 and -2.236067978.Subproblem 1
x + 4 = 2.236067978 Simplifying x + 4 = 2.236067978 Reorder the terms: 4 + x = 2.236067978 Solving 4 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.236067978 + -4 x = 2.236067978 + -4 Combine like terms: 2.236067978 + -4 = -1.763932022 x = -1.763932022 Simplifying x = -1.763932022Subproblem 2
x + 4 = -2.236067978 Simplifying x + 4 = -2.236067978 Reorder the terms: 4 + x = -2.236067978 Solving 4 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.236067978 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.236067978 + -4 x = -2.236067978 + -4 Combine like terms: -2.236067978 + -4 = -6.236067978 x = -6.236067978 Simplifying x = -6.236067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.763932022, -6.236067978}Solution
x = {-1.763932022, -6.236067978}
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