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Simplifying -16t2 + 35t + 12 = 0 Reorder the terms: 12 + 35t + -16t2 = 0 Solving 12 + 35t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.75 + -2.1875t + t2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.1875t + 0.75 + t2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.1875t + t2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.1875t + t2 = 0 + 0.75 -2.1875t + t2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.1875t + t2 = 0.75 The t term is -2.1875t. Take half its coefficient (-1.09375). Square it (1.196289063) and add it to both sides. Add '1.196289063' to each side of the equation. -2.1875t + 1.196289063 + t2 = 0.75 + 1.196289063 Reorder the terms: 1.196289063 + -2.1875t + t2 = 0.75 + 1.196289063 Combine like terms: 0.75 + 1.196289063 = 1.946289063 1.196289063 + -2.1875t + t2 = 1.946289063 Factor a perfect square on the left side: (t + -1.09375)(t + -1.09375) = 1.946289063 Calculate the square root of the right side: 1.395094643 Break this problem into two subproblems by setting (t + -1.09375) equal to 1.395094643 and -1.395094643.Subproblem 1
t + -1.09375 = 1.395094643 Simplifying t + -1.09375 = 1.395094643 Reorder the terms: -1.09375 + t = 1.395094643 Solving -1.09375 + t = 1.395094643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = 1.395094643 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = 1.395094643 + 1.09375 t = 1.395094643 + 1.09375 Combine like terms: 1.395094643 + 1.09375 = 2.488844643 t = 2.488844643 Simplifying t = 2.488844643Subproblem 2
t + -1.09375 = -1.395094643 Simplifying t + -1.09375 = -1.395094643 Reorder the terms: -1.09375 + t = -1.395094643 Solving -1.09375 + t = -1.395094643 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.09375' to each side of the equation. -1.09375 + 1.09375 + t = -1.395094643 + 1.09375 Combine like terms: -1.09375 + 1.09375 = 0.00000 0.00000 + t = -1.395094643 + 1.09375 t = -1.395094643 + 1.09375 Combine like terms: -1.395094643 + 1.09375 = -0.301344643 t = -0.301344643 Simplifying t = -0.301344643Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.488844643, -0.301344643}
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