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Simplifying -4.9t2 + 8.4t + 1.5 = 0 Reorder the terms: 1.5 + 8.4t + -4.9t2 = 0 Solving 1.5 + 8.4t + -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'. -0.306122449 + -1.714285714t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -1.714285714t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -1.714285714t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -1.714285714t + t2 = 0 + 0.306122449 -1.714285714t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -1.714285714t + t2 = 0.306122449 The t term is -1.714285714t. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714t + 0.7346938773 + t2 = 0.306122449 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714t + t2 = 0.306122449 + 0.7346938773 Combine like terms: 0.306122449 + 0.7346938773 = 1.0408163263 0.7346938773 + -1.714285714t + t2 = 1.0408163263 Factor a perfect square on the left side: (t + -0.857142857)(t + -0.857142857) = 1.0408163263 Calculate the square root of the right side: 1.020204061 Break this problem into two subproblems by setting (t + -0.857142857) equal to 1.020204061 and -1.020204061.Subproblem 1
t + -0.857142857 = 1.020204061 Simplifying t + -0.857142857 = 1.020204061 Reorder the terms: -0.857142857 + t = 1.020204061 Solving -0.857142857 + t = 1.020204061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + t = 1.020204061 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + t = 1.020204061 + 0.857142857 t = 1.020204061 + 0.857142857 Combine like terms: 1.020204061 + 0.857142857 = 1.877346918 t = 1.877346918 Simplifying t = 1.877346918Subproblem 2
t + -0.857142857 = -1.020204061 Simplifying t + -0.857142857 = -1.020204061 Reorder the terms: -0.857142857 + t = -1.020204061 Solving -0.857142857 + t = -1.020204061 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + t = -1.020204061 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + t = -1.020204061 + 0.857142857 t = -1.020204061 + 0.857142857 Combine like terms: -1.020204061 + 0.857142857 = -0.163061204 t = -0.163061204 Simplifying t = -0.163061204Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.877346918, -0.163061204}
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