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Simplifying -5t2 + 26t = -45 Reorder the terms: 26t + -5t2 = -45 Solving 26t + -5t2 = -45 Solving for variable 't'. Reorder the terms: 45 + 26t + -5t2 = -45 + 45 Combine like terms: -45 + 45 = 0 45 + 26t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -9 + -5.2t + t2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -5.2t + 9 + t2 = 0 + 9 Reorder the terms: -9 + 9 + -5.2t + t2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5.2t + t2 = 0 + 9 -5.2t + t2 = 0 + 9 Combine like terms: 0 + 9 = 9 -5.2t + t2 = 9 The t term is -5.2t. Take half its coefficient (-2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. -5.2t + 6.76 + t2 = 9 + 6.76 Reorder the terms: 6.76 + -5.2t + t2 = 9 + 6.76 Combine like terms: 9 + 6.76 = 15.76 6.76 + -5.2t + t2 = 15.76 Factor a perfect square on the left side: (t + -2.6)(t + -2.6) = 15.76 Calculate the square root of the right side: 3.969886648 Break this problem into two subproblems by setting (t + -2.6) equal to 3.969886648 and -3.969886648.Subproblem 1
t + -2.6 = 3.969886648 Simplifying t + -2.6 = 3.969886648 Reorder the terms: -2.6 + t = 3.969886648 Solving -2.6 + t = 3.969886648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + t = 3.969886648 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + t = 3.969886648 + 2.6 t = 3.969886648 + 2.6 Combine like terms: 3.969886648 + 2.6 = 6.569886648 t = 6.569886648 Simplifying t = 6.569886648Subproblem 2
t + -2.6 = -3.969886648 Simplifying t + -2.6 = -3.969886648 Reorder the terms: -2.6 + t = -3.969886648 Solving -2.6 + t = -3.969886648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.6' to each side of the equation. -2.6 + 2.6 + t = -3.969886648 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + t = -3.969886648 + 2.6 t = -3.969886648 + 2.6 Combine like terms: -3.969886648 + 2.6 = -1.369886648 t = -1.369886648 Simplifying t = -1.369886648Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.569886648, -1.369886648}
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