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Simplifying -16t2 + 15t + 28 = 0 Reorder the terms: 28 + 15t + -16t2 = 0 Solving 28 + 15t + -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'. -1.75 + -0.9375t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -0.9375t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -0.9375t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -0.9375t + t2 = 0 + 1.75 -0.9375t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -0.9375t + t2 = 1.75 The t term is -0.9375t. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375t + 0.2197265625 + t2 = 1.75 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 1.75 + 0.2197265625 Combine like terms: 1.75 + 0.2197265625 = 1.9697265625 0.2197265625 + -0.9375t + t2 = 1.9697265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 1.9697265625 Calculate the square root of the right side: 1.403469473 Break this problem into two subproblems by setting (t + -0.46875) equal to 1.403469473 and -1.403469473.Subproblem 1
t + -0.46875 = 1.403469473 Simplifying t + -0.46875 = 1.403469473 Reorder the terms: -0.46875 + t = 1.403469473 Solving -0.46875 + t = 1.403469473 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = 1.403469473 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 1.403469473 + 0.46875 t = 1.403469473 + 0.46875 Combine like terms: 1.403469473 + 0.46875 = 1.872219473 t = 1.872219473 Simplifying t = 1.872219473Subproblem 2
t + -0.46875 = -1.403469473 Simplifying t + -0.46875 = -1.403469473 Reorder the terms: -0.46875 + t = -1.403469473 Solving -0.46875 + t = -1.403469473 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.46875' to each side of the equation. -0.46875 + 0.46875 + t = -1.403469473 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -1.403469473 + 0.46875 t = -1.403469473 + 0.46875 Combine like terms: -1.403469473 + 0.46875 = -0.934719473 t = -0.934719473 Simplifying t = -0.934719473Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.872219473, -0.934719473}
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