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Simplifying t2 = 6t + 43 Reorder the terms: t2 = 43 + 6t Solving t2 = 43 + 6t Solving for variable 't'. Reorder the terms: -43 + -6t + t2 = 43 + 6t + -43 + -6t Reorder the terms: -43 + -6t + t2 = 43 + -43 + 6t + -6t Combine like terms: 43 + -43 = 0 -43 + -6t + t2 = 0 + 6t + -6t -43 + -6t + t2 = 6t + -6t Combine like terms: 6t + -6t = 0 -43 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -6t + 43 + t2 = 0 + 43 Reorder the terms: -43 + 43 + -6t + t2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -6t + t2 = 0 + 43 -6t + t2 = 0 + 43 Combine like terms: 0 + 43 = 43 -6t + t2 = 43 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 43 + 9 Reorder the terms: 9 + -6t + t2 = 43 + 9 Combine like terms: 43 + 9 = 52 9 + -6t + t2 = 52 Factor a perfect square on the left side: (t + -3)(t + -3) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (t + -3) equal to 7.211102551 and -7.211102551.Subproblem 1
t + -3 = 7.211102551 Simplifying t + -3 = 7.211102551 Reorder the terms: -3 + t = 7.211102551 Solving -3 + t = 7.211102551 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 7.211102551 + 3 Combine like terms: -3 + 3 = 0 0 + t = 7.211102551 + 3 t = 7.211102551 + 3 Combine like terms: 7.211102551 + 3 = 10.211102551 t = 10.211102551 Simplifying t = 10.211102551Subproblem 2
t + -3 = -7.211102551 Simplifying t + -3 = -7.211102551 Reorder the terms: -3 + t = -7.211102551 Solving -3 + t = -7.211102551 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -7.211102551 + 3 Combine like terms: -3 + 3 = 0 0 + t = -7.211102551 + 3 t = -7.211102551 + 3 Combine like terms: -7.211102551 + 3 = -4.211102551 t = -4.211102551 Simplifying t = -4.211102551Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.211102551, -4.211102551}
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