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Simplifying 3x2 + 21x + 90 = 0 Reorder the terms: 90 + 21x + 3x2 = 0 Solving 90 + 21x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(30 + 7x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(30 + 7x + x2)' equal to zero and attempt to solve: Simplifying 30 + 7x + x2 = 0 Solving 30 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 7x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 7x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 7x + x2 = 0 + -30 7x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 7x + x2 = -30 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 = -30 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -30 + 12.25 Combine like terms: -30 + 12.25 = -17.75 12.25 + 7x + x2 = -17.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -17.75 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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