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Simplifying (t2 + -6t + 7) + (-3t2 + 4t + 2) = 0 Reorder the terms: (7 + -6t + t2) + (-3t2 + 4t + 2) = 0 Remove parenthesis around (7 + -6t + t2) 7 + -6t + t2 + (-3t2 + 4t + 2) = 0 Reorder the terms: 7 + -6t + t2 + (2 + 4t + -3t2) = 0 Remove parenthesis around (2 + 4t + -3t2) 7 + -6t + t2 + 2 + 4t + -3t2 = 0 Reorder the terms: 7 + 2 + -6t + 4t + t2 + -3t2 = 0 Combine like terms: 7 + 2 = 9 9 + -6t + 4t + t2 + -3t2 = 0 Combine like terms: -6t + 4t = -2t 9 + -2t + t2 + -3t2 = 0 Combine like terms: t2 + -3t2 = -2t2 9 + -2t + -2t2 = 0 Solving 9 + -2t + -2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + t + t2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + t + 4.5 + t2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + t + t2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t + t2 = 0 + 4.5 t + t2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 t + t2 = 4.5 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 4.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 1.25 + t2 = 4.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (t + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
t + 0.5 = 2.179449472 Simplifying t + 0.5 = 2.179449472 Reorder the terms: 0.5 + t = 2.179449472 Solving 0.5 + t = 2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.179449472 + -0.5 t = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 t = 1.679449472 Simplifying t = 1.679449472Subproblem 2
t + 0.5 = -2.179449472 Simplifying t + 0.5 = -2.179449472 Reorder the terms: 0.5 + t = -2.179449472 Solving 0.5 + t = -2.179449472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.179449472 + -0.5 t = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 t = -2.679449472 Simplifying t = -2.679449472Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.679449472, -2.679449472}
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