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Simplifying 4.75 = t2 + -6t Reorder the terms: 4.75 = -6t + t2 Solving 4.75 = -6t + t2 Solving for variable 't'. Reorder the terms: 4.75 + 6t + -1t2 = -6t + 6t + t2 + -1t2 Combine like terms: -6t + 6t = 0 4.75 + 6t + -1t2 = 0 + t2 + -1t2 4.75 + 6t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 4.75 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4.75 + -6t + t2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -6t + 4.75 + t2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -6t + t2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -6t + t2 = 0 + 4.75 -6t + t2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -6t + t2 = 4.75 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 = 4.75 + 9 Reorder the terms: 9 + -6t + t2 = 4.75 + 9 Combine like terms: 4.75 + 9 = 13.75 9 + -6t + t2 = 13.75 Factor a perfect square on the left side: (t + -3)(t + -3) = 13.75 Calculate the square root of the right side: 3.708099244 Break this problem into two subproblems by setting (t + -3) equal to 3.708099244 and -3.708099244.Subproblem 1
t + -3 = 3.708099244 Simplifying t + -3 = 3.708099244 Reorder the terms: -3 + t = 3.708099244 Solving -3 + t = 3.708099244 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 = 3.708099244 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.708099244 + 3 t = 3.708099244 + 3 Combine like terms: 3.708099244 + 3 = 6.708099244 t = 6.708099244 Simplifying t = 6.708099244Subproblem 2
t + -3 = -3.708099244 Simplifying t + -3 = -3.708099244 Reorder the terms: -3 + t = -3.708099244 Solving -3 + t = -3.708099244 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 = -3.708099244 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.708099244 + 3 t = -3.708099244 + 3 Combine like terms: -3.708099244 + 3 = -0.708099244 t = -0.708099244 Simplifying t = -0.708099244Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.708099244, -0.708099244}
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