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Simplifying -15t2 + 105t + 10 = 250 Reorder the terms: 10 + 105t + -15t2 = 250 Solving 10 + 105t + -15t2 = 250 Solving for variable 't'. Reorder the terms: 10 + -250 + 105t + -15t2 = 250 + -250 Combine like terms: 10 + -250 = -240 -240 + 105t + -15t2 = 250 + -250 Combine like terms: 250 + -250 = 0 -240 + 105t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-16 + 7t + -1t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-16 + 7t + -1t2)' equal to zero and attempt to solve: Simplifying -16 + 7t + -1t2 = 0 Solving -16 + 7t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 16 + -7t + t2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -7t + -16 + t2 = 0 + -16 Reorder the terms: 16 + -16 + -7t + t2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -7t + t2 = 0 + -16 -7t + t2 = 0 + -16 Combine like terms: 0 + -16 = -16 -7t + t2 = -16 The t term is -7t. 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. -7t + 12.25 + t2 = -16 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -16 + 12.25 Combine like terms: -16 + 12.25 = -3.75 12.25 + -7t + t2 = -3.75 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = -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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