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Simplifying -480t2 + 75t + 12 = 0 Reorder the terms: 12 + 75t + -480t2 = 0 Solving 12 + 75t + -480t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 25t + -160t2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 25t + -160t2)' equal to zero and attempt to solve: Simplifying 4 + 25t + -160t2 = 0 Solving 4 + 25t + -160t2 = 0 Begin completing the square. Divide all terms by -160 the coefficient of the squared term: Divide each side by '-160'. -0.025 + -0.15625t + t2 = 0.0 Move the constant term to the right: Add '0.025' to each side of the equation. -0.025 + -0.15625t + 0.025 + t2 = 0.0 + 0.025 Reorder the terms: -0.025 + 0.025 + -0.15625t + t2 = 0.0 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + -0.15625t + t2 = 0.0 + 0.025 -0.15625t + t2 = 0.0 + 0.025 Combine like terms: 0.0 + 0.025 = 0.025 -0.15625t + t2 = 0.025 The t term is -0.15625t. Take half its coefficient (-0.078125). Square it (0.006103515625) and add it to both sides. Add '0.006103515625' to each side of the equation. -0.15625t + 0.006103515625 + t2 = 0.025 + 0.006103515625 Reorder the terms: 0.006103515625 + -0.15625t + t2 = 0.025 + 0.006103515625 Combine like terms: 0.025 + 0.006103515625 = 0.031103515625 0.006103515625 + -0.15625t + t2 = 0.031103515625 Factor a perfect square on the left side: (t + -0.078125)(t + -0.078125) = 0.031103515625 Calculate the square root of the right side: 0.176361888 Break this problem into two subproblems by setting (t + -0.078125) equal to 0.176361888 and -0.176361888.Subproblem 1
t + -0.078125 = 0.176361888 Simplifying t + -0.078125 = 0.176361888 Reorder the terms: -0.078125 + t = 0.176361888 Solving -0.078125 + t = 0.176361888 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + t = 0.176361888 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + t = 0.176361888 + 0.078125 t = 0.176361888 + 0.078125 Combine like terms: 0.176361888 + 0.078125 = 0.254486888 t = 0.254486888 Simplifying t = 0.254486888Subproblem 2
t + -0.078125 = -0.176361888 Simplifying t + -0.078125 = -0.176361888 Reorder the terms: -0.078125 + t = -0.176361888 Solving -0.078125 + t = -0.176361888 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.078125' to each side of the equation. -0.078125 + 0.078125 + t = -0.176361888 + 0.078125 Combine like terms: -0.078125 + 0.078125 = 0.000000 0.000000 + t = -0.176361888 + 0.078125 t = -0.176361888 + 0.078125 Combine like terms: -0.176361888 + 0.078125 = -0.098236888 t = -0.098236888 Simplifying t = -0.098236888Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.254486888, -0.098236888}Solution
t = {0.254486888, -0.098236888}
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