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Simplifying t2 + -30t + -26 = 0 Reorder the terms: -26 + -30t + t2 = 0 Solving -26 + -30t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -30t + 26 + t2 = 0 + 26 Reorder the terms: -26 + 26 + -30t + t2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -30t + t2 = 0 + 26 -30t + t2 = 0 + 26 Combine like terms: 0 + 26 = 26 -30t + t2 = 26 The t term is -30t. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30t + 225 + t2 = 26 + 225 Reorder the terms: 225 + -30t + t2 = 26 + 225 Combine like terms: 26 + 225 = 251 225 + -30t + t2 = 251 Factor a perfect square on the left side: (t + -15)(t + -15) = 251 Calculate the square root of the right side: 15.842979518 Break this problem into two subproblems by setting (t + -15) equal to 15.842979518 and -15.842979518.Subproblem 1
t + -15 = 15.842979518 Simplifying t + -15 = 15.842979518 Reorder the terms: -15 + t = 15.842979518 Solving -15 + t = 15.842979518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 15.842979518 + 15 Combine like terms: -15 + 15 = 0 0 + t = 15.842979518 + 15 t = 15.842979518 + 15 Combine like terms: 15.842979518 + 15 = 30.842979518 t = 30.842979518 Simplifying t = 30.842979518Subproblem 2
t + -15 = -15.842979518 Simplifying t + -15 = -15.842979518 Reorder the terms: -15 + t = -15.842979518 Solving -15 + t = -15.842979518 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = -15.842979518 + 15 Combine like terms: -15 + 15 = 0 0 + t = -15.842979518 + 15 t = -15.842979518 + 15 Combine like terms: -15.842979518 + 15 = -0.842979518 t = -0.842979518 Simplifying t = -0.842979518Solution
The solution to the problem is based on the solutions from the subproblems. t = {30.842979518, -0.842979518}
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