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Simplifying 5t2 + -12t + -90 = 0 Reorder the terms: -90 + -12t + 5t2 = 0 Solving -90 + -12t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -18 + -2.4t + t2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -2.4t + 18 + t2 = 0 + 18 Reorder the terms: -18 + 18 + -2.4t + t2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -2.4t + t2 = 0 + 18 -2.4t + t2 = 0 + 18 Combine like terms: 0 + 18 = 18 -2.4t + t2 = 18 The t term is -2.4t. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4t + 1.44 + t2 = 18 + 1.44 Reorder the terms: 1.44 + -2.4t + t2 = 18 + 1.44 Combine like terms: 18 + 1.44 = 19.44 1.44 + -2.4t + t2 = 19.44 Factor a perfect square on the left side: (t + -1.2)(t + -1.2) = 19.44 Calculate the square root of the right side: 4.409081537 Break this problem into two subproblems by setting (t + -1.2) equal to 4.409081537 and -4.409081537.Subproblem 1
t + -1.2 = 4.409081537 Simplifying t + -1.2 = 4.409081537 Reorder the terms: -1.2 + t = 4.409081537 Solving -1.2 + t = 4.409081537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = 4.409081537 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = 4.409081537 + 1.2 t = 4.409081537 + 1.2 Combine like terms: 4.409081537 + 1.2 = 5.609081537 t = 5.609081537 Simplifying t = 5.609081537Subproblem 2
t + -1.2 = -4.409081537 Simplifying t + -1.2 = -4.409081537 Reorder the terms: -1.2 + t = -4.409081537 Solving -1.2 + t = -4.409081537 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + t = -4.409081537 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + t = -4.409081537 + 1.2 t = -4.409081537 + 1.2 Combine like terms: -4.409081537 + 1.2 = -3.209081537 t = -3.209081537 Simplifying t = -3.209081537Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.609081537, -3.209081537}
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