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Simplifying 15 + 4t + -1t2 = 0 Solving 15 + 4t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -4t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -4t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -4t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -4t + t2 = 0 + 15 -4t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -4t + t2 = 15 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 15 + 4 Reorder the terms: 4 + -4t + t2 = 15 + 4 Combine like terms: 15 + 4 = 19 4 + -4t + t2 = 19 Factor a perfect square on the left side: (t + -2)(t + -2) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (t + -2) equal to 4.358898944 and -4.358898944.Subproblem 1
t + -2 = 4.358898944 Simplifying t + -2 = 4.358898944 Reorder the terms: -2 + t = 4.358898944 Solving -2 + t = 4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + t = 4.358898944 + 2 t = 4.358898944 + 2 Combine like terms: 4.358898944 + 2 = 6.358898944 t = 6.358898944 Simplifying t = 6.358898944Subproblem 2
t + -2 = -4.358898944 Simplifying t + -2 = -4.358898944 Reorder the terms: -2 + t = -4.358898944 Solving -2 + t = -4.358898944 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -4.358898944 + 2 Combine like terms: -2 + 2 = 0 0 + t = -4.358898944 + 2 t = -4.358898944 + 2 Combine like terms: -4.358898944 + 2 = -2.358898944 t = -2.358898944 Simplifying t = -2.358898944Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.358898944, -2.358898944}
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