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Simplifying 4.9t2 + -3.443t + -0.25 = 0 Reorder the terms: -0.25 + -3.443t + 4.9t2 = 0 Solving -0.25 + -3.443t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.05102040816 + -0.7026530612t + t2 = 0 Move the constant term to the right: Add '0.05102040816' to each side of the equation. -0.05102040816 + -0.7026530612t + 0.05102040816 + t2 = 0 + 0.05102040816 Reorder the terms: -0.05102040816 + 0.05102040816 + -0.7026530612t + t2 = 0 + 0.05102040816 Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000 0.00000000000 + -0.7026530612t + t2 = 0 + 0.05102040816 -0.7026530612t + t2 = 0 + 0.05102040816 Combine like terms: 0 + 0.05102040816 = 0.05102040816 -0.7026530612t + t2 = 0.05102040816 The t term is -0.7026530612t. Take half its coefficient (-0.3513265306). Square it (0.1234303311) and add it to both sides. Add '0.1234303311' to each side of the equation. -0.7026530612t + 0.1234303311 + t2 = 0.05102040816 + 0.1234303311 Reorder the terms: 0.1234303311 + -0.7026530612t + t2 = 0.05102040816 + 0.1234303311 Combine like terms: 0.05102040816 + 0.1234303311 = 0.17445073926 0.1234303311 + -0.7026530612t + t2 = 0.17445073926 Factor a perfect square on the left side: (t + -0.3513265306)(t + -0.3513265306) = 0.17445073926 Calculate the square root of the right side: 0.417673005 Break this problem into two subproblems by setting (t + -0.3513265306) equal to 0.417673005 and -0.417673005.Subproblem 1
t + -0.3513265306 = 0.417673005 Simplifying t + -0.3513265306 = 0.417673005 Reorder the terms: -0.3513265306 + t = 0.417673005 Solving -0.3513265306 + t = 0.417673005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3513265306' to each side of the equation. -0.3513265306 + 0.3513265306 + t = 0.417673005 + 0.3513265306 Combine like terms: -0.3513265306 + 0.3513265306 = 0.0000000000 0.0000000000 + t = 0.417673005 + 0.3513265306 t = 0.417673005 + 0.3513265306 Combine like terms: 0.417673005 + 0.3513265306 = 0.7689995356 t = 0.7689995356 Simplifying t = 0.7689995356Subproblem 2
t + -0.3513265306 = -0.417673005 Simplifying t + -0.3513265306 = -0.417673005 Reorder the terms: -0.3513265306 + t = -0.417673005 Solving -0.3513265306 + t = -0.417673005 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3513265306' to each side of the equation. -0.3513265306 + 0.3513265306 + t = -0.417673005 + 0.3513265306 Combine like terms: -0.3513265306 + 0.3513265306 = 0.0000000000 0.0000000000 + t = -0.417673005 + 0.3513265306 t = -0.417673005 + 0.3513265306 Combine like terms: -0.417673005 + 0.3513265306 = -0.0663464744 t = -0.0663464744 Simplifying t = -0.0663464744Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.7689995356, -0.0663464744}
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