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Simplifying -16t2 + 112t + 210 = t Reorder the terms: 210 + 112t + -16t2 = t Solving 210 + 112t + -16t2 = t Solving for variable 't'. Reorder the terms: 210 + 112t + -1t + -16t2 = t + -1t Combine like terms: 112t + -1t = 111t 210 + 111t + -16t2 = t + -1t Combine like terms: t + -1t = 0 210 + 111t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -13.125 + -6.9375t + t2 = 0 Move the constant term to the right: Add '13.125' to each side of the equation. -13.125 + -6.9375t + 13.125 + t2 = 0 + 13.125 Reorder the terms: -13.125 + 13.125 + -6.9375t + t2 = 0 + 13.125 Combine like terms: -13.125 + 13.125 = 0.000 0.000 + -6.9375t + t2 = 0 + 13.125 -6.9375t + t2 = 0 + 13.125 Combine like terms: 0 + 13.125 = 13.125 -6.9375t + t2 = 13.125 The t term is -6.9375t. Take half its coefficient (-3.46875). Square it (12.03222656) and add it to both sides. Add '12.03222656' to each side of the equation. -6.9375t + 12.03222656 + t2 = 13.125 + 12.03222656 Reorder the terms: 12.03222656 + -6.9375t + t2 = 13.125 + 12.03222656 Combine like terms: 13.125 + 12.03222656 = 25.15722656 12.03222656 + -6.9375t + t2 = 25.15722656 Factor a perfect square on the left side: (t + -3.46875)(t + -3.46875) = 25.15722656 Calculate the square root of the right side: 5.015698013 Break this problem into two subproblems by setting (t + -3.46875) equal to 5.015698013 and -5.015698013.Subproblem 1
t + -3.46875 = 5.015698013 Simplifying t + -3.46875 = 5.015698013 Reorder the terms: -3.46875 + t = 5.015698013 Solving -3.46875 + t = 5.015698013 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.46875' to each side of the equation. -3.46875 + 3.46875 + t = 5.015698013 + 3.46875 Combine like terms: -3.46875 + 3.46875 = 0.00000 0.00000 + t = 5.015698013 + 3.46875 t = 5.015698013 + 3.46875 Combine like terms: 5.015698013 + 3.46875 = 8.484448013 t = 8.484448013 Simplifying t = 8.484448013Subproblem 2
t + -3.46875 = -5.015698013 Simplifying t + -3.46875 = -5.015698013 Reorder the terms: -3.46875 + t = -5.015698013 Solving -3.46875 + t = -5.015698013 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.46875' to each side of the equation. -3.46875 + 3.46875 + t = -5.015698013 + 3.46875 Combine like terms: -3.46875 + 3.46875 = 0.00000 0.00000 + t = -5.015698013 + 3.46875 t = -5.015698013 + 3.46875 Combine like terms: -5.015698013 + 3.46875 = -1.546948013 t = -1.546948013 Simplifying t = -1.546948013Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.484448013, -1.546948013}
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