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Simplifying 4.9t2 + -2.39t + -3.44 = 0 Reorder the terms: -3.44 + -2.39t + 4.9t2 = 0 Solving -3.44 + -2.39t + 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'. -0.7020408163 + -0.487755102t + t2 = 0 Move the constant term to the right: Add '0.7020408163' to each side of the equation. -0.7020408163 + -0.487755102t + 0.7020408163 + t2 = 0 + 0.7020408163 Reorder the terms: -0.7020408163 + 0.7020408163 + -0.487755102t + t2 = 0 + 0.7020408163 Combine like terms: -0.7020408163 + 0.7020408163 = 0.0000000000 0.0000000000 + -0.487755102t + t2 = 0 + 0.7020408163 -0.487755102t + t2 = 0 + 0.7020408163 Combine like terms: 0 + 0.7020408163 = 0.7020408163 -0.487755102t + t2 = 0.7020408163 The t term is -0.487755102t. Take half its coefficient (-0.243877551). Square it (0.05947625988) and add it to both sides. Add '0.05947625988' to each side of the equation. -0.487755102t + 0.05947625988 + t2 = 0.7020408163 + 0.05947625988 Reorder the terms: 0.05947625988 + -0.487755102t + t2 = 0.7020408163 + 0.05947625988 Combine like terms: 0.7020408163 + 0.05947625988 = 0.76151707618 0.05947625988 + -0.487755102t + t2 = 0.76151707618 Factor a perfect square on the left side: (t + -0.243877551)(t + -0.243877551) = 0.76151707618 Calculate the square root of the right side: 0.872649458 Break this problem into two subproblems by setting (t + -0.243877551) equal to 0.872649458 and -0.872649458.Subproblem 1
t + -0.243877551 = 0.872649458 Simplifying t + -0.243877551 = 0.872649458 Reorder the terms: -0.243877551 + t = 0.872649458 Solving -0.243877551 + t = 0.872649458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.243877551' to each side of the equation. -0.243877551 + 0.243877551 + t = 0.872649458 + 0.243877551 Combine like terms: -0.243877551 + 0.243877551 = 0.000000000 0.000000000 + t = 0.872649458 + 0.243877551 t = 0.872649458 + 0.243877551 Combine like terms: 0.872649458 + 0.243877551 = 1.116527009 t = 1.116527009 Simplifying t = 1.116527009Subproblem 2
t + -0.243877551 = -0.872649458 Simplifying t + -0.243877551 = -0.872649458 Reorder the terms: -0.243877551 + t = -0.872649458 Solving -0.243877551 + t = -0.872649458 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.243877551' to each side of the equation. -0.243877551 + 0.243877551 + t = -0.872649458 + 0.243877551 Combine like terms: -0.243877551 + 0.243877551 = 0.000000000 0.000000000 + t = -0.872649458 + 0.243877551 t = -0.872649458 + 0.243877551 Combine like terms: -0.872649458 + 0.243877551 = -0.628771907 t = -0.628771907 Simplifying t = -0.628771907Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.116527009, -0.628771907}
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