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Simplifying -16t2 + 20t + 7 = 0 Reorder the terms: 7 + 20t + -16t2 = 0 Solving 7 + 20t + -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'. -0.4375 + -1.25t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -1.25t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -1.25t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -1.25t + t2 = 0 + 0.4375 -1.25t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -1.25t + t2 = 0.4375 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 0.4375 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 0.4375 + 0.390625 Combine like terms: 0.4375 + 0.390625 = 0.828125 0.390625 + -1.25t + t2 = 0.828125 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 0.828125 Calculate the square root of the right side: 0.910013736 Break this problem into two subproblems by setting (t + -0.625) equal to 0.910013736 and -0.910013736.Subproblem 1
t + -0.625 = 0.910013736 Simplifying t + -0.625 = 0.910013736 Reorder the terms: -0.625 + t = 0.910013736 Solving -0.625 + t = 0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 0.910013736 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 0.910013736 + 0.625 t = 0.910013736 + 0.625 Combine like terms: 0.910013736 + 0.625 = 1.535013736 t = 1.535013736 Simplifying t = 1.535013736Subproblem 2
t + -0.625 = -0.910013736 Simplifying t + -0.625 = -0.910013736 Reorder the terms: -0.625 + t = -0.910013736 Solving -0.625 + t = -0.910013736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -0.910013736 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -0.910013736 + 0.625 t = -0.910013736 + 0.625 Combine like terms: -0.910013736 + 0.625 = -0.285013736 t = -0.285013736 Simplifying t = -0.285013736Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.535013736, -0.285013736}
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