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Simplifying 0 = -16t2 + -112t + 84 Reorder the terms: 0 = 84 + -112t + -16t2 Solving 0 = 84 + -112t + -16t2 Solving for variable 't'. Combine like terms: 0 + -84 = -84 -84 + 112t + 16t2 = 84 + -112t + -16t2 + -84 + 112t + 16t2 Reorder the terms: -84 + 112t + 16t2 = 84 + -84 + -112t + 112t + -16t2 + 16t2 Combine like terms: 84 + -84 = 0 -84 + 112t + 16t2 = 0 + -112t + 112t + -16t2 + 16t2 -84 + 112t + 16t2 = -112t + 112t + -16t2 + 16t2 Combine like terms: -112t + 112t = 0 -84 + 112t + 16t2 = 0 + -16t2 + 16t2 -84 + 112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -84 + 112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-21 + 28t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-21 + 28t + 4t2)' equal to zero and attempt to solve: Simplifying -21 + 28t + 4t2 = 0 Solving -21 + 28t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.25 + 7t + t2 = 0 Move the constant term to the right: Add '5.25' to each side of the equation. -5.25 + 7t + 5.25 + t2 = 0 + 5.25 Reorder the terms: -5.25 + 5.25 + 7t + t2 = 0 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + 7t + t2 = 0 + 5.25 7t + t2 = 0 + 5.25 Combine like terms: 0 + 5.25 = 5.25 7t + t2 = 5.25 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = 5.25 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 5.25 + 12.25 Combine like terms: 5.25 + 12.25 = 17.5 12.25 + 7t + t2 = 17.5 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 17.5 Calculate the square root of the right side: 4.183300133 Break this problem into two subproblems by setting (t + 3.5) equal to 4.183300133 and -4.183300133.Subproblem 1
t + 3.5 = 4.183300133 Simplifying t + 3.5 = 4.183300133 Reorder the terms: 3.5 + t = 4.183300133 Solving 3.5 + t = 4.183300133 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = 4.183300133 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 4.183300133 + -3.5 t = 4.183300133 + -3.5 Combine like terms: 4.183300133 + -3.5 = 0.683300133 t = 0.683300133 Simplifying t = 0.683300133Subproblem 2
t + 3.5 = -4.183300133 Simplifying t + 3.5 = -4.183300133 Reorder the terms: 3.5 + t = -4.183300133 Solving 3.5 + t = -4.183300133 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = -4.183300133 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -4.183300133 + -3.5 t = -4.183300133 + -3.5 Combine like terms: -4.183300133 + -3.5 = -7.683300133 t = -7.683300133 Simplifying t = -7.683300133Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.683300133, -7.683300133}Solution
t = {0.683300133, -7.683300133}
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