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Simplifying 3x2 + 6x + 15x + 120 = 0 Reorder the terms: 120 + 6x + 15x + 3x2 = 0 Combine like terms: 6x + 15x = 21x 120 + 21x + 3x2 = 0 Solving 120 + 21x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(40 + 7x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(40 + 7x + x2)' equal to zero and attempt to solve: Simplifying 40 + 7x + x2 = 0 Solving 40 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 7x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 7x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 7x + x2 = 0 + -40 7x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 7x + x2 = -40 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 = -40 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -40 + 12.25 Combine like terms: -40 + 12.25 = -27.75 12.25 + 7x + x2 = -27.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -27.75 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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