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Simplifying 0 = -16t2 + 10t + 56 Reorder the terms: 0 = 56 + 10t + -16t2 Solving 0 = 56 + 10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -56 = -56 -56 + -10t + 16t2 = 56 + 10t + -16t2 + -56 + -10t + 16t2 Reorder the terms: -56 + -10t + 16t2 = 56 + -56 + 10t + -10t + -16t2 + 16t2 Combine like terms: 56 + -56 = 0 -56 + -10t + 16t2 = 0 + 10t + -10t + -16t2 + 16t2 -56 + -10t + 16t2 = 10t + -10t + -16t2 + 16t2 Combine like terms: 10t + -10t = 0 -56 + -10t + 16t2 = 0 + -16t2 + 16t2 -56 + -10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -56 + -10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -5t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -5t + 8t2)' equal to zero and attempt to solve: Simplifying -28 + -5t + 8t2 = 0 Solving -28 + -5t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.5 + -0.625t + t2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -0.625t + 3.5 + t2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -0.625t + t2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -0.625t + t2 = 0 + 3.5 -0.625t + t2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -0.625t + t2 = 3.5 The t term is -0.625t. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625t + 0.09765625 + t2 = 3.5 + 0.09765625 Reorder the terms: 0.09765625 + -0.625t + t2 = 3.5 + 0.09765625 Combine like terms: 3.5 + 0.09765625 = 3.59765625 0.09765625 + -0.625t + t2 = 3.59765625 Factor a perfect square on the left side: (t + -0.3125)(t + -0.3125) = 3.59765625 Calculate the square root of the right side: 1.896748863 Break this problem into two subproblems by setting (t + -0.3125) equal to 1.896748863 and -1.896748863.Subproblem 1
t + -0.3125 = 1.896748863 Simplifying t + -0.3125 = 1.896748863 Reorder the terms: -0.3125 + t = 1.896748863 Solving -0.3125 + t = 1.896748863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = 1.896748863 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = 1.896748863 + 0.3125 t = 1.896748863 + 0.3125 Combine like terms: 1.896748863 + 0.3125 = 2.209248863 t = 2.209248863 Simplifying t = 2.209248863Subproblem 2
t + -0.3125 = -1.896748863 Simplifying t + -0.3125 = -1.896748863 Reorder the terms: -0.3125 + t = -1.896748863 Solving -0.3125 + t = -1.896748863 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + t = -1.896748863 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + t = -1.896748863 + 0.3125 t = -1.896748863 + 0.3125 Combine like terms: -1.896748863 + 0.3125 = -1.584248863 t = -1.584248863 Simplifying t = -1.584248863Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.209248863, -1.584248863}Solution
t = {2.209248863, -1.584248863}
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