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Simplifying 5t2 + -14t + -7 = 0 Reorder the terms: -7 + -14t + 5t2 = 0 Solving -7 + -14t + 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'. -1.4 + -2.8t + t2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -2.8t + 1.4 + t2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -2.8t + t2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -2.8t + t2 = 0 + 1.4 -2.8t + t2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -2.8t + t2 = 1.4 The t term is -2.8t. Take half its coefficient (-1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. -2.8t + 1.96 + t2 = 1.4 + 1.96 Reorder the terms: 1.96 + -2.8t + t2 = 1.4 + 1.96 Combine like terms: 1.4 + 1.96 = 3.36 1.96 + -2.8t + t2 = 3.36 Factor a perfect square on the left side: (t + -1.4)(t + -1.4) = 3.36 Calculate the square root of the right side: 1.833030278 Break this problem into two subproblems by setting (t + -1.4) equal to 1.833030278 and -1.833030278.Subproblem 1
t + -1.4 = 1.833030278 Simplifying t + -1.4 = 1.833030278 Reorder the terms: -1.4 + t = 1.833030278 Solving -1.4 + t = 1.833030278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = 1.833030278 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = 1.833030278 + 1.4 t = 1.833030278 + 1.4 Combine like terms: 1.833030278 + 1.4 = 3.233030278 t = 3.233030278 Simplifying t = 3.233030278Subproblem 2
t + -1.4 = -1.833030278 Simplifying t + -1.4 = -1.833030278 Reorder the terms: -1.4 + t = -1.833030278 Solving -1.4 + t = -1.833030278 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.4' to each side of the equation. -1.4 + 1.4 + t = -1.833030278 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + t = -1.833030278 + 1.4 t = -1.833030278 + 1.4 Combine like terms: -1.833030278 + 1.4 = -0.433030278 t = -0.433030278 Simplifying t = -0.433030278Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.233030278, -0.433030278}
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