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Simplifying 10x2 + 105x + 360 = 0 Reorder the terms: 360 + 105x + 10x2 = 0 Solving 360 + 105x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(72 + 21x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(72 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying 72 + 21x + 2x2 = 0 Solving 72 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 36 + 10.5x + x2 = 0 Move the constant term to the right: Add '-36' to each side of the equation. 36 + 10.5x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 10.5x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 10.5x + x2 = 0 + -36 10.5x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 10.5x + x2 = -36 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = -36 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -36 + 27.5625 Combine like terms: -36 + 27.5625 = -8.4375 27.5625 + 10.5x + x2 = -8.4375 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = -8.4375 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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