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Simplifying -16t2 + 56t + 4 = 0 Reorder the terms: 4 + 56t + -16t2 = 0 Solving 4 + 56t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 14t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 14t + -4t2)' equal to zero and attempt to solve: Simplifying 1 + 14t + -4t2 = 0 Solving 1 + 14t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -3.5t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.5t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.5t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.5t + t2 = 0 + 0.25 -3.5t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.5t + t2 = 0.25 The t term is -3.5t. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5t + 3.0625 + t2 = 0.25 + 3.0625 Reorder the terms: 3.0625 + -3.5t + t2 = 0.25 + 3.0625 Combine like terms: 0.25 + 3.0625 = 3.3125 3.0625 + -3.5t + t2 = 3.3125 Factor a perfect square on the left side: (t + -1.75)(t + -1.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (t + -1.75) equal to 1.820027472 and -1.820027472.Subproblem 1
t + -1.75 = 1.820027472 Simplifying t + -1.75 = 1.820027472 Reorder the terms: -1.75 + t = 1.820027472 Solving -1.75 + t = 1.820027472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = 1.820027472 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = 1.820027472 + 1.75 t = 1.820027472 + 1.75 Combine like terms: 1.820027472 + 1.75 = 3.570027472 t = 3.570027472 Simplifying t = 3.570027472Subproblem 2
t + -1.75 = -1.820027472 Simplifying t + -1.75 = -1.820027472 Reorder the terms: -1.75 + t = -1.820027472 Solving -1.75 + t = -1.820027472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + t = -1.820027472 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + t = -1.820027472 + 1.75 t = -1.820027472 + 1.75 Combine like terms: -1.820027472 + 1.75 = -0.070027472 t = -0.070027472 Simplifying t = -0.070027472Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.570027472, -0.070027472}Solution
t = {3.570027472, -0.070027472}
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