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Simplifying 0 = 2x2 + 10x + 26 Reorder the terms: 0 = 26 + 10x + 2x2 Solving 0 = 26 + 10x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -26 = -26 -26 + -10x + -2x2 = 26 + 10x + 2x2 + -26 + -10x + -2x2 Reorder the terms: -26 + -10x + -2x2 = 26 + -26 + 10x + -10x + 2x2 + -2x2 Combine like terms: 26 + -26 = 0 -26 + -10x + -2x2 = 0 + 10x + -10x + 2x2 + -2x2 -26 + -10x + -2x2 = 10x + -10x + 2x2 + -2x2 Combine like terms: 10x + -10x = 0 -26 + -10x + -2x2 = 0 + 2x2 + -2x2 -26 + -10x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -26 + -10x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(13 + 5x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(13 + 5x + x2)' equal to zero and attempt to solve: Simplifying 13 + 5x + x2 = 0 Solving 13 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 5x + -13 + x2 = 0 + -13 Reorder the terms: 13 + -13 + 5x + x2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 5x + x2 = 0 + -13 5x + x2 = 0 + -13 Combine like terms: 0 + -13 = -13 5x + x2 = -13 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 = -13 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -13 + 6.25 Combine like terms: -13 + 6.25 = -6.75 6.25 + 5x + x2 = -6.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -6.75 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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