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Simplifying 8t2 + -8t + -450 = 0 Reorder the terms: -450 + -8t + 8t2 = 0 Solving -450 + -8t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + -4t + 4t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + -4t + 4t2)' equal to zero and attempt to solve: Simplifying -225 + -4t + 4t2 = 0 Solving -225 + -4t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -56.25 + -1t + t2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + -1t + 56.25 + t2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + -1t + t2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + -1t + t2 = 0 + 56.25 -1t + t2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 -1t + t2 = 56.25 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 56.25 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 56.25 + 0.25 Combine like terms: 56.25 + 0.25 = 56.5 0.25 + -1t + t2 = 56.5 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 56.5 Calculate the square root of the right side: 7.516648189 Break this problem into two subproblems by setting (t + -0.5) equal to 7.516648189 and -7.516648189.Subproblem 1
t + -0.5 = 7.516648189 Simplifying t + -0.5 = 7.516648189 Reorder the terms: -0.5 + t = 7.516648189 Solving -0.5 + t = 7.516648189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 7.516648189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 7.516648189 + 0.5 t = 7.516648189 + 0.5 Combine like terms: 7.516648189 + 0.5 = 8.016648189 t = 8.016648189 Simplifying t = 8.016648189Subproblem 2
t + -0.5 = -7.516648189 Simplifying t + -0.5 = -7.516648189 Reorder the terms: -0.5 + t = -7.516648189 Solving -0.5 + t = -7.516648189 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -7.516648189 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -7.516648189 + 0.5 t = -7.516648189 + 0.5 Combine like terms: -7.516648189 + 0.5 = -7.016648189 t = -7.016648189 Simplifying t = -7.016648189Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.016648189, -7.016648189}Solution
t = {8.016648189, -7.016648189}
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