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Simplifying 0 = x2 + 5x + 130 Reorder the terms: 0 = 130 + 5x + x2 Solving 0 = 130 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + -130 = -130 -130 + -5x + -1x2 = 130 + 5x + x2 + -130 + -5x + -1x2 Reorder the terms: -130 + -5x + -1x2 = 130 + -130 + 5x + -5x + x2 + -1x2 Combine like terms: 130 + -130 = 0 -130 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 -130 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 -130 + -5x + -1x2 = 0 + x2 + -1x2 -130 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -130 + -5x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(130 + 5x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(130 + 5x + x2)' equal to zero and attempt to solve: Simplifying 130 + 5x + x2 = 0 Solving 130 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-130' to each side of the equation. 130 + 5x + -130 + x2 = 0 + -130 Reorder the terms: 130 + -130 + 5x + x2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + 5x + x2 = 0 + -130 5x + x2 = 0 + -130 Combine like terms: 0 + -130 = -130 5x + x2 = -130 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -130 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -130 + 6.25 Combine like terms: -130 + 6.25 = -123.75 6.25 + 5x + x2 = -123.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -123.75 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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