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Simplifying 218 = 13t2 + -73t Reorder the terms: 218 = -73t + 13t2 Solving 218 = -73t + 13t2 Solving for variable 't'. Reorder the terms: 218 + 73t + -13t2 = -73t + 73t + 13t2 + -13t2 Combine like terms: -73t + 73t = 0 218 + 73t + -13t2 = 0 + 13t2 + -13t2 218 + 73t + -13t2 = 13t2 + -13t2 Combine like terms: 13t2 + -13t2 = 0 218 + 73t + -13t2 = 0 Begin completing the square. Divide all terms by -13 the coefficient of the squared term: Divide each side by '-13'. -16.76923077 + -5.615384615t + t2 = 0 Move the constant term to the right: Add '16.76923077' to each side of the equation. -16.76923077 + -5.615384615t + 16.76923077 + t2 = 0 + 16.76923077 Reorder the terms: -16.76923077 + 16.76923077 + -5.615384615t + t2 = 0 + 16.76923077 Combine like terms: -16.76923077 + 16.76923077 = 0.00000000 0.00000000 + -5.615384615t + t2 = 0 + 16.76923077 -5.615384615t + t2 = 0 + 16.76923077 Combine like terms: 0 + 16.76923077 = 16.76923077 -5.615384615t + t2 = 16.76923077 The t term is -5.615384615t. Take half its coefficient (-2.807692308). Square it (7.883136096) and add it to both sides. Add '7.883136096' to each side of the equation. -5.615384615t + 7.883136096 + t2 = 16.76923077 + 7.883136096 Reorder the terms: 7.883136096 + -5.615384615t + t2 = 16.76923077 + 7.883136096 Combine like terms: 16.76923077 + 7.883136096 = 24.652366866 7.883136096 + -5.615384615t + t2 = 24.652366866 Factor a perfect square on the left side: (t + -2.807692308)(t + -2.807692308) = 24.652366866 Calculate the square root of the right side: 4.96511499 Break this problem into two subproblems by setting (t + -2.807692308) equal to 4.96511499 and -4.96511499.Subproblem 1
t + -2.807692308 = 4.96511499 Simplifying t + -2.807692308 = 4.96511499 Reorder the terms: -2.807692308 + t = 4.96511499 Solving -2.807692308 + t = 4.96511499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.807692308' to each side of the equation. -2.807692308 + 2.807692308 + t = 4.96511499 + 2.807692308 Combine like terms: -2.807692308 + 2.807692308 = 0.000000000 0.000000000 + t = 4.96511499 + 2.807692308 t = 4.96511499 + 2.807692308 Combine like terms: 4.96511499 + 2.807692308 = 7.772807298 t = 7.772807298 Simplifying t = 7.772807298Subproblem 2
t + -2.807692308 = -4.96511499 Simplifying t + -2.807692308 = -4.96511499 Reorder the terms: -2.807692308 + t = -4.96511499 Solving -2.807692308 + t = -4.96511499 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.807692308' to each side of the equation. -2.807692308 + 2.807692308 + t = -4.96511499 + 2.807692308 Combine like terms: -2.807692308 + 2.807692308 = 0.000000000 0.000000000 + t = -4.96511499 + 2.807692308 t = -4.96511499 + 2.807692308 Combine like terms: -4.96511499 + 2.807692308 = -2.157422682 t = -2.157422682 Simplifying t = -2.157422682Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.772807298, -2.157422682}
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