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Simplifying 5t2 + -6t + -28 = 0 Reorder the terms: -28 + -6t + 5t2 = 0 Solving -28 + -6t + 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'. -5.6 + -1.2t + t2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -1.2t + 5.6 + t2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -1.2t + t2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -1.2t + t2 = 0 + 5.6 -1.2t + t2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -1.2t + t2 = 5.6 The t term is -1.2t. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2t + 0.36 + t2 = 5.6 + 0.36 Reorder the terms: 0.36 + -1.2t + t2 = 5.6 + 0.36 Combine like terms: 5.6 + 0.36 = 5.96 0.36 + -1.2t + t2 = 5.96 Factor a perfect square on the left side: (t + -0.6)(t + -0.6) = 5.96 Calculate the square root of the right side: 2.441311123 Break this problem into two subproblems by setting (t + -0.6) equal to 2.441311123 and -2.441311123.Subproblem 1
t + -0.6 = 2.441311123 Simplifying t + -0.6 = 2.441311123 Reorder the terms: -0.6 + t = 2.441311123 Solving -0.6 + t = 2.441311123 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = 2.441311123 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = 2.441311123 + 0.6 t = 2.441311123 + 0.6 Combine like terms: 2.441311123 + 0.6 = 3.041311123 t = 3.041311123 Simplifying t = 3.041311123Subproblem 2
t + -0.6 = -2.441311123 Simplifying t + -0.6 = -2.441311123 Reorder the terms: -0.6 + t = -2.441311123 Solving -0.6 + t = -2.441311123 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = -2.441311123 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = -2.441311123 + 0.6 t = -2.441311123 + 0.6 Combine like terms: -2.441311123 + 0.6 = -1.841311123 t = -1.841311123 Simplifying t = -1.841311123Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.041311123, -1.841311123}
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