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Simplifying 13x + 2x2 + 20 = 3x Reorder the terms: 20 + 13x + 2x2 = 3x Solving 20 + 13x + 2x2 = 3x Solving for variable 'x'. Reorder the terms: 20 + 13x + -3x + 2x2 = 3x + -3x Combine like terms: 13x + -3x = 10x 20 + 10x + 2x2 = 3x + -3x Combine like terms: 3x + -3x = 0 20 + 10x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 5x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 5x + x2)' equal to zero and attempt to solve: Simplifying 10 + 5x + x2 = 0 Solving 10 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 5x + x2 = 0 + -10 5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 5x + x2 = -10 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 = -10 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -10 + 6.25 Combine like terms: -10 + 6.25 = -3.75 6.25 + 5x + x2 = -3.75 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = -3.75 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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