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Simplifying -16t2 + 45t + 10 = 0 Reorder the terms: 10 + 45t + -16t2 = 0 Solving 10 + 45t + -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'. -0.625 + -2.8125t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2.8125t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2.8125t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2.8125t + t2 = 0 + 0.625 -2.8125t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2.8125t + t2 = 0.625 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 0.625 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 0.625 + 1.977539063 Combine like terms: 0.625 + 1.977539063 = 2.602539063 1.977539063 + -2.8125t + t2 = 2.602539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 2.602539063 Calculate the square root of the right side: 1.613238688 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.613238688 and -1.613238688.Subproblem 1
t + -1.40625 = 1.613238688 Simplifying t + -1.40625 = 1.613238688 Reorder the terms: -1.40625 + t = 1.613238688 Solving -1.40625 + t = 1.613238688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 1.613238688 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.613238688 + 1.40625 t = 1.613238688 + 1.40625 Combine like terms: 1.613238688 + 1.40625 = 3.019488688 t = 3.019488688 Simplifying t = 3.019488688Subproblem 2
t + -1.40625 = -1.613238688 Simplifying t + -1.40625 = -1.613238688 Reorder the terms: -1.40625 + t = -1.613238688 Solving -1.40625 + t = -1.613238688 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -1.613238688 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.613238688 + 1.40625 t = -1.613238688 + 1.40625 Combine like terms: -1.613238688 + 1.40625 = -0.206988688 t = -0.206988688 Simplifying t = -0.206988688Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.019488688, -0.206988688}
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