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Simplifying 30 = 8.13t + 5t2 Solving 30 = 8.13t + 5t2 Solving for variable 't'. Reorder the terms: 30 + -8.13t + -5t2 = 8.13t + -8.13t + 5t2 + -5t2 Combine like terms: 8.13t + -8.13t = 0.00 30 + -8.13t + -5t2 = 0.00 + 5t2 + -5t2 30 + -8.13t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 30 + -8.13t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6 + 1.626t + t2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.626t + 6 + t2 = 0 + 6 Reorder the terms: -6 + 6 + 1.626t + t2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.626t + t2 = 0 + 6 1.626t + t2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.626t + t2 = 6 The t term is 1.626t. Take half its coefficient (0.813). Square it (0.660969) and add it to both sides. Add '0.660969' to each side of the equation. 1.626t + 0.660969 + t2 = 6 + 0.660969 Reorder the terms: 0.660969 + 1.626t + t2 = 6 + 0.660969 Combine like terms: 6 + 0.660969 = 6.660969 0.660969 + 1.626t + t2 = 6.660969 Factor a perfect square on the left side: (t + 0.813)(t + 0.813) = 6.660969 Calculate the square root of the right side: 2.580885313 Break this problem into two subproblems by setting (t + 0.813) equal to 2.580885313 and -2.580885313.Subproblem 1
t + 0.813 = 2.580885313 Simplifying t + 0.813 = 2.580885313 Reorder the terms: 0.813 + t = 2.580885313 Solving 0.813 + t = 2.580885313 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.813' to each side of the equation. 0.813 + -0.813 + t = 2.580885313 + -0.813 Combine like terms: 0.813 + -0.813 = 0.000 0.000 + t = 2.580885313 + -0.813 t = 2.580885313 + -0.813 Combine like terms: 2.580885313 + -0.813 = 1.767885313 t = 1.767885313 Simplifying t = 1.767885313Subproblem 2
t + 0.813 = -2.580885313 Simplifying t + 0.813 = -2.580885313 Reorder the terms: 0.813 + t = -2.580885313 Solving 0.813 + t = -2.580885313 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.813' to each side of the equation. 0.813 + -0.813 + t = -2.580885313 + -0.813 Combine like terms: 0.813 + -0.813 = 0.000 0.000 + t = -2.580885313 + -0.813 t = -2.580885313 + -0.813 Combine like terms: -2.580885313 + -0.813 = -3.393885313 t = -3.393885313 Simplifying t = -3.393885313Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.767885313, -3.393885313}
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