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Simplifying (5t * t) + -1(4t) + -4200 = 0 Multiply t * t (5t2) + -1(4t) + -4200 = 0 Remove parenthesis around (4t) (5t2) + -1 * 4t + -4200 = 0 Multiply -1 * 4 (5t2) + -4t + -4200 = 0 Reorder the terms: -4200 + -4t + (5t2) = 0 Solving -4200 + -4t + (5t2) = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -840 + -0.8t + t2 = 0 Move the constant term to the right: Add '840' to each side of the equation. -840 + -0.8t + 840 + t2 = 0 + 840 Reorder the terms: -840 + 840 + -0.8t + t2 = 0 + 840 Combine like terms: -840 + 840 = 0 0 + -0.8t + t2 = 0 + 840 -0.8t + t2 = 0 + 840 Combine like terms: 0 + 840 = 840 -0.8t + t2 = 840 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 840 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 840 + 0.16 Combine like terms: 840 + 0.16 = 840.16 0.16 + -0.8t + t2 = 840.16 Factor a perfect square on the left side: ((t) + -0.4)((t) + -0.4) = 840.16 Calculate the square root of the right side: 28.985513623 Break this problem into two subproblems by setting ((t) + -0.4) equal to 28.985513623 and -28.985513623.Subproblem 1
(t) + -0.4 = 28.985513623 Simplifying (t) + -0.4 = 28.985513623 t + -0.4 = 28.985513623 Reorder the terms: -0.4 + t = 28.985513623 Solving -0.4 + t = 28.985513623 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 28.985513623 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 28.985513623 + 0.4 t = 28.985513623 + 0.4 Combine like terms: 28.985513623 + 0.4 = 29.385513623 t = 29.385513623 Simplifying t = 29.385513623Subproblem 2
(t) + -0.4 = -28.985513623 Simplifying (t) + -0.4 = -28.985513623 t + -0.4 = -28.985513623 Reorder the terms: -0.4 + t = -28.985513623 Solving -0.4 + t = -28.985513623 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -28.985513623 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -28.985513623 + 0.4 t = -28.985513623 + 0.4 Combine like terms: -28.985513623 + 0.4 = -28.585513623 t = -28.585513623 Simplifying t = -28.585513623Solution
The solution to the problem is based on the solutions from the subproblems. t = {29.385513623, -28.585513623}
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