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Simplifying 7 = -16t(-16t) + 30t + 6 Remove parenthesis around (-16t) 7 = -16t * -16t + 30t + 6 Reorder the terms for easier multiplication: 7 = -16 * -16t * t + 30t + 6 Multiply -16 * -16 7 = 256t * t + 30t + 6 Multiply t * t 7 = 256t2 + 30t + 6 Reorder the terms: 7 = 6 + 30t + 256t2 Solving 7 = 6 + 30t + 256t2 Solving for variable 't'. Combine like terms: 7 + -6 = 1 1 + -30t + -256t2 = 6 + 30t + 256t2 + -6 + -30t + -256t2 Reorder the terms: 1 + -30t + -256t2 = 6 + -6 + 30t + -30t + 256t2 + -256t2 Combine like terms: 6 + -6 = 0 1 + -30t + -256t2 = 0 + 30t + -30t + 256t2 + -256t2 1 + -30t + -256t2 = 30t + -30t + 256t2 + -256t2 Combine like terms: 30t + -30t = 0 1 + -30t + -256t2 = 0 + 256t2 + -256t2 1 + -30t + -256t2 = 256t2 + -256t2 Combine like terms: 256t2 + -256t2 = 0 1 + -30t + -256t2 = 0 Begin completing the square. Divide all terms by -256 the coefficient of the squared term: Divide each side by '-256'. -0.00390625 + 0.1171875t + t2 = 0 Move the constant term to the right: Add '0.00390625' to each side of the equation. -0.00390625 + 0.1171875t + 0.00390625 + t2 = 0 + 0.00390625 Reorder the terms: -0.00390625 + 0.00390625 + 0.1171875t + t2 = 0 + 0.00390625 Combine like terms: -0.00390625 + 0.00390625 = 0.00000000 0.00000000 + 0.1171875t + t2 = 0 + 0.00390625 0.1171875t + t2 = 0 + 0.00390625 Combine like terms: 0 + 0.00390625 = 0.00390625 0.1171875t + t2 = 0.00390625 The t term is 0.1171875t. Take half its coefficient (0.05859375). Square it (0.003433227539) and add it to both sides. Add '0.003433227539' to each side of the equation. 0.1171875t + 0.003433227539 + t2 = 0.00390625 + 0.003433227539 Reorder the terms: 0.003433227539 + 0.1171875t + t2 = 0.00390625 + 0.003433227539 Combine like terms: 0.00390625 + 0.003433227539 = 0.007339477539 0.003433227539 + 0.1171875t + t2 = 0.007339477539 Factor a perfect square on the left side: (t + 0.05859375)(t + 0.05859375) = 0.007339477539 Calculate the square root of the right side: 0.085670751 Break this problem into two subproblems by setting (t + 0.05859375) equal to 0.085670751 and -0.085670751.Subproblem 1
t + 0.05859375 = 0.085670751 Simplifying t + 0.05859375 = 0.085670751 Reorder the terms: 0.05859375 + t = 0.085670751 Solving 0.05859375 + t = 0.085670751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05859375' to each side of the equation. 0.05859375 + -0.05859375 + t = 0.085670751 + -0.05859375 Combine like terms: 0.05859375 + -0.05859375 = 0.00000000 0.00000000 + t = 0.085670751 + -0.05859375 t = 0.085670751 + -0.05859375 Combine like terms: 0.085670751 + -0.05859375 = 0.027077001 t = 0.027077001 Simplifying t = 0.027077001Subproblem 2
t + 0.05859375 = -0.085670751 Simplifying t + 0.05859375 = -0.085670751 Reorder the terms: 0.05859375 + t = -0.085670751 Solving 0.05859375 + t = -0.085670751 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05859375' to each side of the equation. 0.05859375 + -0.05859375 + t = -0.085670751 + -0.05859375 Combine like terms: 0.05859375 + -0.05859375 = 0.00000000 0.00000000 + t = -0.085670751 + -0.05859375 t = -0.085670751 + -0.05859375 Combine like terms: -0.085670751 + -0.05859375 = -0.144264501 t = -0.144264501 Simplifying t = -0.144264501Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.027077001, -0.144264501}
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