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Simplifying -5t2 + -5t + 90 = 0 Reorder the terms: 90 + -5t + -5t2 = 0 Solving 90 + -5t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(18 + -1t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(18 + -1t + -1t2)' equal to zero and attempt to solve: Simplifying 18 + -1t + -1t2 = 0 Solving 18 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + t + t2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + t + 18 + t2 = 0 + 18 Reorder the terms: -18 + 18 + t + t2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + t + t2 = 0 + 18 t + t2 = 0 + 18 Combine like terms: 0 + 18 = 18 t + t2 = 18 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 18 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 1.25 + t2 = 18.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (t + 0.5) equal to 4.272001873 and -4.272001873.Subproblem 1
t + 0.5 = 4.272001873 Simplifying t + 0.5 = 4.272001873 Reorder the terms: 0.5 + t = 4.272001873 Solving 0.5 + t = 4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 4.272001873 + -0.5 t = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 t = 3.772001873 Simplifying t = 3.772001873Subproblem 2
t + 0.5 = -4.272001873 Simplifying t + 0.5 = -4.272001873 Reorder the terms: 0.5 + t = -4.272001873 Solving 0.5 + t = -4.272001873 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -4.272001873 + -0.5 t = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 t = -4.772001873 Simplifying t = -4.772001873Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.772001873, -4.772001873}Solution
t = {3.772001873, -4.772001873}
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