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Simplifying 130 = (16t * t) + 27t Multiply t * t 130 = (16t2) + 27t Reorder the terms: 130 = 27t + (16t2) Solving 130 = 27t + (16t2) Solving for variable 't'. Reorder the terms: 130 + -27t + (-16t2) = 27t + -27t + (16t2) + (-16t2) Combine like terms: 27t + -27t = 0 130 + -27t + (-16t2) = 0 + (16t2) + (-16t2) 130 + -27t + (-16t2) = (16t2) + (-16t2) Combine like terms: (16t2) + (-16t2) = 0 130 + -27t + (-16t2) = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -8.125 + 1.6875t + t2 = 0 Move the constant term to the right: Add '8.125' to each side of the equation. -8.125 + 1.6875t + 8.125 + t2 = 0 + 8.125 Reorder the terms: -8.125 + 8.125 + 1.6875t + t2 = 0 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + 1.6875t + t2 = 0 + 8.125 1.6875t + t2 = 0 + 8.125 Combine like terms: 0 + 8.125 = 8.125 1.6875t + t2 = 8.125 The t term is 1.6875t. Take half its coefficient (0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. 1.6875t + 0.7119140625 + t2 = 8.125 + 0.7119140625 Reorder the terms: 0.7119140625 + 1.6875t + t2 = 8.125 + 0.7119140625 Combine like terms: 8.125 + 0.7119140625 = 8.8369140625 0.7119140625 + 1.6875t + t2 = 8.8369140625 Factor a perfect square on the left side: ((t) + 0.84375)((t) + 0.84375) = 8.8369140625 Calculate the square root of the right side: 2.972694748 Break this problem into two subproblems by setting ((t) + 0.84375) equal to 2.972694748 and -2.972694748.Subproblem 1
(t) + 0.84375 = 2.972694748 Simplifying (t) + 0.84375 = 2.972694748 t + 0.84375 = 2.972694748 Reorder the terms: 0.84375 + t = 2.972694748 Solving 0.84375 + t = 2.972694748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + t = 2.972694748 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + t = 2.972694748 + -0.84375 t = 2.972694748 + -0.84375 Combine like terms: 2.972694748 + -0.84375 = 2.128944748 t = 2.128944748 Simplifying t = 2.128944748Subproblem 2
(t) + 0.84375 = -2.972694748 Simplifying (t) + 0.84375 = -2.972694748 t + 0.84375 = -2.972694748 Reorder the terms: 0.84375 + t = -2.972694748 Solving 0.84375 + t = -2.972694748 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.84375' to each side of the equation. 0.84375 + -0.84375 + t = -2.972694748 + -0.84375 Combine like terms: 0.84375 + -0.84375 = 0.00000 0.00000 + t = -2.972694748 + -0.84375 t = -2.972694748 + -0.84375 Combine like terms: -2.972694748 + -0.84375 = -3.816444748 t = -3.816444748 Simplifying t = -3.816444748Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.128944748, -3.816444748}
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