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Simplifying -16t2 + 58t + 3 = 0 Reorder the terms: 3 + 58t + -16t2 = 0 Solving 3 + 58t + -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'. -0.1875 + -3.625t + t2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + -3.625t + 0.1875 + t2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + -3.625t + t2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + -3.625t + t2 = 0 + 0.1875 -3.625t + t2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 -3.625t + t2 = 0.1875 The t term is -3.625t. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625t + 3.28515625 + t2 = 0.1875 + 3.28515625 Reorder the terms: 3.28515625 + -3.625t + t2 = 0.1875 + 3.28515625 Combine like terms: 0.1875 + 3.28515625 = 3.47265625 3.28515625 + -3.625t + t2 = 3.47265625 Factor a perfect square on the left side: (t + -1.8125)(t + -1.8125) = 3.47265625 Calculate the square root of the right side: 1.863506439 Break this problem into two subproblems by setting (t + -1.8125) equal to 1.863506439 and -1.863506439.Subproblem 1
t + -1.8125 = 1.863506439 Simplifying t + -1.8125 = 1.863506439 Reorder the terms: -1.8125 + t = 1.863506439 Solving -1.8125 + t = 1.863506439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + t = 1.863506439 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + t = 1.863506439 + 1.8125 t = 1.863506439 + 1.8125 Combine like terms: 1.863506439 + 1.8125 = 3.676006439 t = 3.676006439 Simplifying t = 3.676006439Subproblem 2
t + -1.8125 = -1.863506439 Simplifying t + -1.8125 = -1.863506439 Reorder the terms: -1.8125 + t = -1.863506439 Solving -1.8125 + t = -1.863506439 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + t = -1.863506439 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + t = -1.863506439 + 1.8125 t = -1.863506439 + 1.8125 Combine like terms: -1.863506439 + 1.8125 = -0.051006439 t = -0.051006439 Simplifying t = -0.051006439Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.676006439, -0.051006439}
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