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Simplifying 4 * 9t2 + 15t + -25 = 0 Multiply 4 * 9 36t2 + 15t + -25 = 0 Reorder the terms: -25 + 15t + 36t2 = 0 Solving -25 + 15t + 36t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.6944444444 + 0.4166666667t + t2 = 0 Move the constant term to the right: Add '0.6944444444' to each side of the equation. -0.6944444444 + 0.4166666667t + 0.6944444444 + t2 = 0 + 0.6944444444 Reorder the terms: -0.6944444444 + 0.6944444444 + 0.4166666667t + t2 = 0 + 0.6944444444 Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000 0.0000000000 + 0.4166666667t + t2 = 0 + 0.6944444444 0.4166666667t + t2 = 0 + 0.6944444444 Combine like terms: 0 + 0.6944444444 = 0.6944444444 0.4166666667t + t2 = 0.6944444444 The t term is 0.4166666667t. Take half its coefficient (0.2083333334). Square it (0.04340277781) and add it to both sides. Add '0.04340277781' to each side of the equation. 0.4166666667t + 0.04340277781 + t2 = 0.6944444444 + 0.04340277781 Reorder the terms: 0.04340277781 + 0.4166666667t + t2 = 0.6944444444 + 0.04340277781 Combine like terms: 0.6944444444 + 0.04340277781 = 0.73784722221 0.04340277781 + 0.4166666667t + t2 = 0.73784722221 Factor a perfect square on the left side: (t + 0.2083333334)(t + 0.2083333334) = 0.73784722221 Calculate the square root of the right side: 0.858980339 Break this problem into two subproblems by setting (t + 0.2083333334) equal to 0.858980339 and -0.858980339.Subproblem 1
t + 0.2083333334 = 0.858980339 Simplifying t + 0.2083333334 = 0.858980339 Reorder the terms: 0.2083333334 + t = 0.858980339 Solving 0.2083333334 + t = 0.858980339 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + t = 0.858980339 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + t = 0.858980339 + -0.2083333334 t = 0.858980339 + -0.2083333334 Combine like terms: 0.858980339 + -0.2083333334 = 0.6506470056 t = 0.6506470056 Simplifying t = 0.6506470056Subproblem 2
t + 0.2083333334 = -0.858980339 Simplifying t + 0.2083333334 = -0.858980339 Reorder the terms: 0.2083333334 + t = -0.858980339 Solving 0.2083333334 + t = -0.858980339 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2083333334' to each side of the equation. 0.2083333334 + -0.2083333334 + t = -0.858980339 + -0.2083333334 Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000 0.0000000000 + t = -0.858980339 + -0.2083333334 t = -0.858980339 + -0.2083333334 Combine like terms: -0.858980339 + -0.2083333334 = -1.0673136724 t = -1.0673136724 Simplifying t = -1.0673136724Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6506470056, -1.0673136724}
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