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Simplifying -490 = 70t + -5t2 Solving -490 = 70t + -5t2 Solving for variable 't'. Reorder the terms: -490 + -70t + 5t2 = 70t + -70t + -5t2 + 5t2 Combine like terms: 70t + -70t = 0 -490 + -70t + 5t2 = 0 + -5t2 + 5t2 -490 + -70t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -490 + -70t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-98 + -14t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-98 + -14t + t2)' equal to zero and attempt to solve: Simplifying -98 + -14t + t2 = 0 Solving -98 + -14t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -14t + 98 + t2 = 0 + 98 Reorder the terms: -98 + 98 + -14t + t2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -14t + t2 = 0 + 98 -14t + t2 = 0 + 98 Combine like terms: 0 + 98 = 98 -14t + t2 = 98 The t term is -14t. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14t + 49 + t2 = 98 + 49 Reorder the terms: 49 + -14t + t2 = 98 + 49 Combine like terms: 98 + 49 = 147 49 + -14t + t2 = 147 Factor a perfect square on the left side: (t + -7)(t + -7) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (t + -7) equal to 12.124355653 and -12.124355653.Subproblem 1
t + -7 = 12.124355653 Simplifying t + -7 = 12.124355653 Reorder the terms: -7 + t = 12.124355653 Solving -7 + t = 12.124355653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = 12.124355653 + 7 Combine like terms: -7 + 7 = 0 0 + t = 12.124355653 + 7 t = 12.124355653 + 7 Combine like terms: 12.124355653 + 7 = 19.124355653 t = 19.124355653 Simplifying t = 19.124355653Subproblem 2
t + -7 = -12.124355653 Simplifying t + -7 = -12.124355653 Reorder the terms: -7 + t = -12.124355653 Solving -7 + t = -12.124355653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + t = -12.124355653 + 7 Combine like terms: -7 + 7 = 0 0 + t = -12.124355653 + 7 t = -12.124355653 + 7 Combine like terms: -12.124355653 + 7 = -5.124355653 t = -5.124355653 Simplifying t = -5.124355653Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.124355653, -5.124355653}Solution
t = {19.124355653, -5.124355653}
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