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Simplifying -1x + -52 = x2 + 6x + 6 Reorder the terms: -52 + -1x = x2 + 6x + 6 Reorder the terms: -52 + -1x = 6 + 6x + x2 Solving -52 + -1x = 6 + 6x + x2 Solving for variable 'x'. Reorder the terms: -52 + -6 + -1x + -6x + -1x2 = 6 + 6x + x2 + -6 + -6x + -1x2 Combine like terms: -52 + -6 = -58 -58 + -1x + -6x + -1x2 = 6 + 6x + x2 + -6 + -6x + -1x2 Combine like terms: -1x + -6x = -7x -58 + -7x + -1x2 = 6 + 6x + x2 + -6 + -6x + -1x2 Reorder the terms: -58 + -7x + -1x2 = 6 + -6 + 6x + -6x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -58 + -7x + -1x2 = 0 + 6x + -6x + x2 + -1x2 -58 + -7x + -1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -58 + -7x + -1x2 = 0 + x2 + -1x2 -58 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -58 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(58 + 7x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(58 + 7x + x2)' equal to zero and attempt to solve: Simplifying 58 + 7x + x2 = 0 Solving 58 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-58' to each side of the equation. 58 + 7x + -58 + x2 = 0 + -58 Reorder the terms: 58 + -58 + 7x + x2 = 0 + -58 Combine like terms: 58 + -58 = 0 0 + 7x + x2 = 0 + -58 7x + x2 = 0 + -58 Combine like terms: 0 + -58 = -58 7x + x2 = -58 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -58 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -58 + 12.25 Combine like terms: -58 + 12.25 = -45.75 12.25 + 7x + x2 = -45.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -45.75 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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