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Simplifying 4t + -2 + t2 = 6 + 7 Reorder the terms: -2 + 4t + t2 = 6 + 7 Combine like terms: 6 + 7 = 13 -2 + 4t + t2 = 13 Solving -2 + 4t + t2 = 13 Solving for variable 't'. Reorder the terms: -2 + -13 + 4t + t2 = 13 + -13 Combine like terms: -2 + -13 = -15 -15 + 4t + t2 = 13 + -13 Combine like terms: 13 + -13 = 0 -15 + 4t + t2 = 0 Begin completing the square. 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 = 2.358898944 t = 2.358898944 Simplifying t = 2.358898944Subproblem 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 = -6.358898944 t = -6.358898944 Simplifying t = -6.358898944Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.358898944, -6.358898944}
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