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Simplifying -4.9t2 + 7t + 0.6 = 0 Reorder the terms: 0.6 + 7t + -4.9t2 = 0 Solving 0.6 + 7t + -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'. -0.1224489796 + -1.428571429t + t2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + -1.428571429t + 0.1224489796 + t2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + -1.428571429t + t2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + -1.428571429t + t2 = 0 + 0.1224489796 -1.428571429t + t2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 -1.428571429t + t2 = 0.1224489796 The t term is -1.428571429t. Take half its coefficient (-0.7142857145). Square it (0.5102040819) and add it to both sides. Add '0.5102040819' to each side of the equation. -1.428571429t + 0.5102040819 + t2 = 0.1224489796 + 0.5102040819 Reorder the terms: 0.5102040819 + -1.428571429t + t2 = 0.1224489796 + 0.5102040819 Combine like terms: 0.1224489796 + 0.5102040819 = 0.6326530615 0.5102040819 + -1.428571429t + t2 = 0.6326530615 Factor a perfect square on the left side: (t + -0.7142857145)(t + -0.7142857145) = 0.6326530615 Calculate the square root of the right side: 0.795394909 Break this problem into two subproblems by setting (t + -0.7142857145) equal to 0.795394909 and -0.795394909.Subproblem 1
t + -0.7142857145 = 0.795394909 Simplifying t + -0.7142857145 = 0.795394909 Reorder the terms: -0.7142857145 + t = 0.795394909 Solving -0.7142857145 + t = 0.795394909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = 0.795394909 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = 0.795394909 + 0.7142857145 t = 0.795394909 + 0.7142857145 Combine like terms: 0.795394909 + 0.7142857145 = 1.5096806235 t = 1.5096806235 Simplifying t = 1.5096806235Subproblem 2
t + -0.7142857145 = -0.795394909 Simplifying t + -0.7142857145 = -0.795394909 Reorder the terms: -0.7142857145 + t = -0.795394909 Solving -0.7142857145 + t = -0.795394909 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7142857145' to each side of the equation. -0.7142857145 + 0.7142857145 + t = -0.795394909 + 0.7142857145 Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000 0.0000000000 + t = -0.795394909 + 0.7142857145 t = -0.795394909 + 0.7142857145 Combine like terms: -0.795394909 + 0.7142857145 = -0.0811091945 t = -0.0811091945 Simplifying t = -0.0811091945Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5096806235, -0.0811091945}
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