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Simplifying (x + 3) + (x + 11) = x(x + 8) + 57 Reorder the terms: (3 + x) + (x + 11) = x(x + 8) + 57 Remove parenthesis around (3 + x) 3 + x + (x + 11) = x(x + 8) + 57 Reorder the terms: 3 + x + (11 + x) = x(x + 8) + 57 Remove parenthesis around (11 + x) 3 + x + 11 + x = x(x + 8) + 57 Reorder the terms: 3 + 11 + x + x = x(x + 8) + 57 Combine like terms: 3 + 11 = 14 14 + x + x = x(x + 8) + 57 Combine like terms: x + x = 2x 14 + 2x = x(x + 8) + 57 Reorder the terms: 14 + 2x = x(8 + x) + 57 14 + 2x = (8 * x + x * x) + 57 14 + 2x = (8x + x2) + 57 Reorder the terms: 14 + 2x = 57 + 8x + x2 Solving 14 + 2x = 57 + 8x + x2 Solving for variable 'x'. Reorder the terms: 14 + -57 + 2x + -8x + -1x2 = 57 + 8x + x2 + -57 + -8x + -1x2 Combine like terms: 14 + -57 = -43 -43 + 2x + -8x + -1x2 = 57 + 8x + x2 + -57 + -8x + -1x2 Combine like terms: 2x + -8x = -6x -43 + -6x + -1x2 = 57 + 8x + x2 + -57 + -8x + -1x2 Reorder the terms: -43 + -6x + -1x2 = 57 + -57 + 8x + -8x + x2 + -1x2 Combine like terms: 57 + -57 = 0 -43 + -6x + -1x2 = 0 + 8x + -8x + x2 + -1x2 -43 + -6x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -43 + -6x + -1x2 = 0 + x2 + -1x2 -43 + -6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -43 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(43 + 6x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(43 + 6x + x2)' equal to zero and attempt to solve: Simplifying 43 + 6x + x2 = 0 Solving 43 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-43' to each side of the equation. 43 + 6x + -43 + x2 = 0 + -43 Reorder the terms: 43 + -43 + 6x + x2 = 0 + -43 Combine like terms: 43 + -43 = 0 0 + 6x + x2 = 0 + -43 6x + x2 = 0 + -43 Combine like terms: 0 + -43 = -43 6x + x2 = -43 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -43 + 9 Reorder the terms: 9 + 6x + x2 = -43 + 9 Combine like terms: -43 + 9 = -34 9 + 6x + x2 = -34 Factor a perfect square on the left side: (x + 3)(x + 3) = -34 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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