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Simplifying 5t2 + -7t + -4 = 0 Reorder the terms: -4 + -7t + 5t2 = 0 Solving -4 + -7t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + -1.4t + t2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + -1.4t + 0.8 + t2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + -1.4t + t2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + -1.4t + t2 = 0 + 0.8 -1.4t + t2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 -1.4t + t2 = 0.8 The t term is -1.4t. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4t + 0.49 + t2 = 0.8 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = 0.8 + 0.49 Combine like terms: 0.8 + 0.49 = 1.29 0.49 + -1.4t + t2 = 1.29 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (t + -0.7) equal to 1.135781669 and -1.135781669.Subproblem 1
t + -0.7 = 1.135781669 Simplifying t + -0.7 = 1.135781669 Reorder the terms: -0.7 + t = 1.135781669 Solving -0.7 + t = 1.135781669 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 1.135781669 + 0.7 t = 1.135781669 + 0.7 Combine like terms: 1.135781669 + 0.7 = 1.835781669 t = 1.835781669 Simplifying t = 1.835781669Subproblem 2
t + -0.7 = -1.135781669 Simplifying t + -0.7 = -1.135781669 Reorder the terms: -0.7 + t = -1.135781669 Solving -0.7 + t = -1.135781669 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -1.135781669 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -1.135781669 + 0.7 t = -1.135781669 + 0.7 Combine like terms: -1.135781669 + 0.7 = -0.435781669 t = -0.435781669 Simplifying t = -0.435781669Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.835781669, -0.435781669}
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