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Simplifying -16t2 + 90t + 70 = 0 Reorder the terms: 70 + 90t + -16t2 = 0 Solving 70 + 90t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + 45t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + 45t + -8t2)' equal to zero and attempt to solve: Simplifying 35 + 45t + -8t2 = 0 Solving 35 + 45t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.375 + -5.625t + t2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + -5.625t + 4.375 + t2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + -5.625t + t2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + -5.625t + t2 = 0 + 4.375 -5.625t + t2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 -5.625t + t2 = 4.375 The t term is -5.625t. Take half its coefficient (-2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. -5.625t + 7.91015625 + t2 = 4.375 + 7.91015625 Reorder the terms: 7.91015625 + -5.625t + t2 = 4.375 + 7.91015625 Combine like terms: 4.375 + 7.91015625 = 12.28515625 7.91015625 + -5.625t + t2 = 12.28515625 Factor a perfect square on the left side: (t + -2.8125)(t + -2.8125) = 12.28515625 Calculate the square root of the right side: 3.505018723 Break this problem into two subproblems by setting (t + -2.8125) equal to 3.505018723 and -3.505018723.Subproblem 1
t + -2.8125 = 3.505018723 Simplifying t + -2.8125 = 3.505018723 Reorder the terms: -2.8125 + t = 3.505018723 Solving -2.8125 + t = 3.505018723 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = 3.505018723 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = 3.505018723 + 2.8125 t = 3.505018723 + 2.8125 Combine like terms: 3.505018723 + 2.8125 = 6.317518723 t = 6.317518723 Simplifying t = 6.317518723Subproblem 2
t + -2.8125 = -3.505018723 Simplifying t + -2.8125 = -3.505018723 Reorder the terms: -2.8125 + t = -3.505018723 Solving -2.8125 + t = -3.505018723 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.8125' to each side of the equation. -2.8125 + 2.8125 + t = -3.505018723 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + t = -3.505018723 + 2.8125 t = -3.505018723 + 2.8125 Combine like terms: -3.505018723 + 2.8125 = -0.692518723 t = -0.692518723 Simplifying t = -0.692518723Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.317518723, -0.692518723}Solution
t = {6.317518723, -0.692518723}
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