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Simplifying -16t2 + 7t + 10 = 0 Reorder the terms: 10 + 7t + -16t2 = 0 Solving 10 + 7t + -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 + -0.4375t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -0.4375t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -0.4375t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -0.4375t + t2 = 0 + 0.625 -0.4375t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -0.4375t + t2 = 0.625 The t term is -0.4375t. Take half its coefficient (-0.21875). Square it (0.0478515625) and add it to both sides. Add '0.0478515625' to each side of the equation. -0.4375t + 0.0478515625 + t2 = 0.625 + 0.0478515625 Reorder the terms: 0.0478515625 + -0.4375t + t2 = 0.625 + 0.0478515625 Combine like terms: 0.625 + 0.0478515625 = 0.6728515625 0.0478515625 + -0.4375t + t2 = 0.6728515625 Factor a perfect square on the left side: (t + -0.21875)(t + -0.21875) = 0.6728515625 Calculate the square root of the right side: 0.820275297 Break this problem into two subproblems by setting (t + -0.21875) equal to 0.820275297 and -0.820275297.Subproblem 1
t + -0.21875 = 0.820275297 Simplifying t + -0.21875 = 0.820275297 Reorder the terms: -0.21875 + t = 0.820275297 Solving -0.21875 + t = 0.820275297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = 0.820275297 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = 0.820275297 + 0.21875 t = 0.820275297 + 0.21875 Combine like terms: 0.820275297 + 0.21875 = 1.039025297 t = 1.039025297 Simplifying t = 1.039025297Subproblem 2
t + -0.21875 = -0.820275297 Simplifying t + -0.21875 = -0.820275297 Reorder the terms: -0.21875 + t = -0.820275297 Solving -0.21875 + t = -0.820275297 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.21875' to each side of the equation. -0.21875 + 0.21875 + t = -0.820275297 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + t = -0.820275297 + 0.21875 t = -0.820275297 + 0.21875 Combine like terms: -0.820275297 + 0.21875 = -0.601525297 t = -0.601525297 Simplifying t = -0.601525297Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.039025297, -0.601525297}
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