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Simplifying 0 = 1.4t2 + -4t + 2.8 Reorder the terms: 0 = 2.8 + -4t + 1.4t2 Solving 0 = 2.8 + -4t + 1.4t2 Solving for variable 't'. Combine like terms: 0 + -2.8 = -2.8 -2.8 + 4t + -1.4t2 = 2.8 + -4t + 1.4t2 + -2.8 + 4t + -1.4t2 Reorder the terms: -2.8 + 4t + -1.4t2 = 2.8 + -2.8 + -4t + 4t + 1.4t2 + -1.4t2 Combine like terms: 2.8 + -2.8 = 0.0 -2.8 + 4t + -1.4t2 = 0.0 + -4t + 4t + 1.4t2 + -1.4t2 -2.8 + 4t + -1.4t2 = -4t + 4t + 1.4t2 + -1.4t2 Combine like terms: -4t + 4t = 0 -2.8 + 4t + -1.4t2 = 0 + 1.4t2 + -1.4t2 -2.8 + 4t + -1.4t2 = 1.4t2 + -1.4t2 Combine like terms: 1.4t2 + -1.4t2 = 0.0 -2.8 + 4t + -1.4t2 = 0.0 Begin completing the square. Divide all terms by -1.4 the coefficient of the squared term: Divide each side by '-1.4'. 2 + -2.857142857t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2.857142857t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -2.857142857t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2.857142857t + t2 = 0 + -2 -2.857142857t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2.857142857t + t2 = -2 The t term is -2.857142857t. Take half its coefficient (-1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. -2.857142857t + 2.040816328 + t2 = -2 + 2.040816328 Reorder the terms: 2.040816328 + -2.857142857t + t2 = -2 + 2.040816328 Combine like terms: -2 + 2.040816328 = 0.040816328 2.040816328 + -2.857142857t + t2 = 0.040816328 Factor a perfect square on the left side: (t + -1.428571429)(t + -1.428571429) = 0.040816328 Calculate the square root of the right side: 0.202030513 Break this problem into two subproblems by setting (t + -1.428571429) equal to 0.202030513 and -0.202030513.Subproblem 1
t + -1.428571429 = 0.202030513 Simplifying t + -1.428571429 = 0.202030513 Reorder the terms: -1.428571429 + t = 0.202030513 Solving -1.428571429 + t = 0.202030513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = 0.202030513 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = 0.202030513 + 1.428571429 t = 0.202030513 + 1.428571429 Combine like terms: 0.202030513 + 1.428571429 = 1.630601942 t = 1.630601942 Simplifying t = 1.630601942Subproblem 2
t + -1.428571429 = -0.202030513 Simplifying t + -1.428571429 = -0.202030513 Reorder the terms: -1.428571429 + t = -0.202030513 Solving -1.428571429 + t = -0.202030513 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + t = -0.202030513 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + t = -0.202030513 + 1.428571429 t = -0.202030513 + 1.428571429 Combine like terms: -0.202030513 + 1.428571429 = 1.226540916 t = 1.226540916 Simplifying t = 1.226540916Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.630601942, 1.226540916}
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