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Simplifying 42 = 6 + 29t + 5t2 Solving 42 = 6 + 29t + 5t2 Solving for variable 't'. Combine like terms: 42 + -6 = 36 36 + -29t + -5t2 = 6 + 29t + 5t2 + -6 + -29t + -5t2 Reorder the terms: 36 + -29t + -5t2 = 6 + -6 + 29t + -29t + 5t2 + -5t2 Combine like terms: 6 + -6 = 0 36 + -29t + -5t2 = 0 + 29t + -29t + 5t2 + -5t2 36 + -29t + -5t2 = 29t + -29t + 5t2 + -5t2 Combine like terms: 29t + -29t = 0 36 + -29t + -5t2 = 0 + 5t2 + -5t2 36 + -29t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 36 + -29t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -7.2 + 5.8t + t2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + 5.8t + 7.2 + t2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + 5.8t + t2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + 5.8t + t2 = 0 + 7.2 5.8t + t2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 5.8t + t2 = 7.2 The t term is 5.8t. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8t + 8.41 + t2 = 7.2 + 8.41 Reorder the terms: 8.41 + 5.8t + t2 = 7.2 + 8.41 Combine like terms: 7.2 + 8.41 = 15.61 8.41 + 5.8t + t2 = 15.61 Factor a perfect square on the left side: (t + 2.9)(t + 2.9) = 15.61 Calculate the square root of the right side: 3.950949253 Break this problem into two subproblems by setting (t + 2.9) equal to 3.950949253 and -3.950949253.Subproblem 1
t + 2.9 = 3.950949253 Simplifying t + 2.9 = 3.950949253 Reorder the terms: 2.9 + t = 3.950949253 Solving 2.9 + t = 3.950949253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + t = 3.950949253 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + t = 3.950949253 + -2.9 t = 3.950949253 + -2.9 Combine like terms: 3.950949253 + -2.9 = 1.050949253 t = 1.050949253 Simplifying t = 1.050949253Subproblem 2
t + 2.9 = -3.950949253 Simplifying t + 2.9 = -3.950949253 Reorder the terms: 2.9 + t = -3.950949253 Solving 2.9 + t = -3.950949253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + t = -3.950949253 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + t = -3.950949253 + -2.9 t = -3.950949253 + -2.9 Combine like terms: -3.950949253 + -2.9 = -6.850949253 t = -6.850949253 Simplifying t = -6.850949253Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.050949253, -6.850949253}
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