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Simplifying (405x2 + 12500 + -3900x) = 0 Reorder the terms: (12500 + -3900x + 405x2) = 0 Remove parenthesis around (12500 + -3900x + 405x2) 12500 + -3900x + 405x2 = 0 Solving 12500 + -3900x + 405x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2500 + -780x + 81x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2500 + -780x + 81x2)' equal to zero and attempt to solve: Simplifying 2500 + -780x + 81x2 = 0 Solving 2500 + -780x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 30.86419753 + -9.62962963x + x2 = 0 Move the constant term to the right: Add '-30.86419753' to each side of the equation. 30.86419753 + -9.62962963x + -30.86419753 + x2 = 0 + -30.86419753 Reorder the terms: 30.86419753 + -30.86419753 + -9.62962963x + x2 = 0 + -30.86419753 Combine like terms: 30.86419753 + -30.86419753 = 0.00000000 0.00000000 + -9.62962963x + x2 = 0 + -30.86419753 -9.62962963x + x2 = 0 + -30.86419753 Combine like terms: 0 + -30.86419753 = -30.86419753 -9.62962963x + x2 = -30.86419753 The x term is -9.62962963x. Take half its coefficient (-4.814814815). Square it (23.18244170) and add it to both sides. Add '23.18244170' to each side of the equation. -9.62962963x + 23.18244170 + x2 = -30.86419753 + 23.18244170 Reorder the terms: 23.18244170 + -9.62962963x + x2 = -30.86419753 + 23.18244170 Combine like terms: -30.86419753 + 23.18244170 = -7.68175583 23.18244170 + -9.62962963x + x2 = -7.68175583 Factor a perfect square on the left side: (x + -4.814814815)(x + -4.814814815) = -7.68175583 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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