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Simplifying 5t2 + -4t + -3 = 4 Reorder the terms: -3 + -4t + 5t2 = 4 Solving -3 + -4t + 5t2 = 4 Solving for variable 't'. Reorder the terms: -3 + -4 + -4t + 5t2 = 4 + -4 Combine like terms: -3 + -4 = -7 -7 + -4t + 5t2 = 4 + -4 Combine like terms: 4 + -4 = 0 -7 + -4t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + -0.8t + t2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.8t + 1.4 + t2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.8t + t2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.8t + t2 = 0 + 1.4 -0.8t + t2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.8t + t2 = 1.4 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 1.4 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 1.4 + 0.16 Combine like terms: 1.4 + 0.16 = 1.56 0.16 + -0.8t + t2 = 1.56 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 1.56 Calculate the square root of the right side: 1.2489996 Break this problem into two subproblems by setting (t + -0.4) equal to 1.2489996 and -1.2489996.Subproblem 1
t + -0.4 = 1.2489996 Simplifying t + -0.4 = 1.2489996 Reorder the terms: -0.4 + t = 1.2489996 Solving -0.4 + t = 1.2489996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 1.2489996 + 0.4 t = 1.2489996 + 0.4 Combine like terms: 1.2489996 + 0.4 = 1.6489996 t = 1.6489996 Simplifying t = 1.6489996Subproblem 2
t + -0.4 = -1.2489996 Simplifying t + -0.4 = -1.2489996 Reorder the terms: -0.4 + t = -1.2489996 Solving -0.4 + t = -1.2489996 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -1.2489996 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -1.2489996 + 0.4 t = -1.2489996 + 0.4 Combine like terms: -1.2489996 + 0.4 = -0.8489996 t = -0.8489996 Simplifying t = -0.8489996Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6489996, -0.8489996}
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