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Simplifying 4t2 + -25t + 15 = 0 Reorder the terms: 15 + -25t + 4t2 = 0 Solving 15 + -25t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.75 + -6.25t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -6.25t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -6.25t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -6.25t + t2 = 0 + -3.75 -6.25t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -6.25t + t2 = -3.75 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = -3.75 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = -3.75 + 9.765625 Combine like terms: -3.75 + 9.765625 = 6.015625 9.765625 + -6.25t + t2 = 6.015625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 6.015625 Calculate the square root of the right side: 2.452677109 Break this problem into two subproblems by setting (t + -3.125) equal to 2.452677109 and -2.452677109.Subproblem 1
t + -3.125 = 2.452677109 Simplifying t + -3.125 = 2.452677109 Reorder the terms: -3.125 + t = 2.452677109 Solving -3.125 + t = 2.452677109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 2.452677109 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 2.452677109 + 3.125 t = 2.452677109 + 3.125 Combine like terms: 2.452677109 + 3.125 = 5.577677109 t = 5.577677109 Simplifying t = 5.577677109Subproblem 2
t + -3.125 = -2.452677109 Simplifying t + -3.125 = -2.452677109 Reorder the terms: -3.125 + t = -2.452677109 Solving -3.125 + t = -2.452677109 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -2.452677109 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -2.452677109 + 3.125 t = -2.452677109 + 3.125 Combine like terms: -2.452677109 + 3.125 = 0.672322891 t = 0.672322891 Simplifying t = 0.672322891Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.577677109, 0.672322891}
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