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Simplifying 7t2 + -62t + 9 = 0 Reorder the terms: 9 + -62t + 7t2 = 0 Solving 9 + -62t + 7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.285714286 + -8.857142857t + t2 = 0 Move the constant term to the right: Add '-1.285714286' to each side of the equation. 1.285714286 + -8.857142857t + -1.285714286 + t2 = 0 + -1.285714286 Reorder the terms: 1.285714286 + -1.285714286 + -8.857142857t + t2 = 0 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + -8.857142857t + t2 = 0 + -1.285714286 -8.857142857t + t2 = 0 + -1.285714286 Combine like terms: 0 + -1.285714286 = -1.285714286 -8.857142857t + t2 = -1.285714286 The t term is -8.857142857t. Take half its coefficient (-4.428571429). Square it (19.61224490) and add it to both sides. Add '19.61224490' to each side of the equation. -8.857142857t + 19.61224490 + t2 = -1.285714286 + 19.61224490 Reorder the terms: 19.61224490 + -8.857142857t + t2 = -1.285714286 + 19.61224490 Combine like terms: -1.285714286 + 19.61224490 = 18.326530614 19.61224490 + -8.857142857t + t2 = 18.326530614 Factor a perfect square on the left side: (t + -4.428571429)(t + -4.428571429) = 18.326530614 Calculate the square root of the right side: 4.280949733 Break this problem into two subproblems by setting (t + -4.428571429) equal to 4.280949733 and -4.280949733.Subproblem 1
t + -4.428571429 = 4.280949733 Simplifying t + -4.428571429 = 4.280949733 Reorder the terms: -4.428571429 + t = 4.280949733 Solving -4.428571429 + t = 4.280949733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.428571429' to each side of the equation. -4.428571429 + 4.428571429 + t = 4.280949733 + 4.428571429 Combine like terms: -4.428571429 + 4.428571429 = 0.000000000 0.000000000 + t = 4.280949733 + 4.428571429 t = 4.280949733 + 4.428571429 Combine like terms: 4.280949733 + 4.428571429 = 8.709521162 t = 8.709521162 Simplifying t = 8.709521162Subproblem 2
t + -4.428571429 = -4.280949733 Simplifying t + -4.428571429 = -4.280949733 Reorder the terms: -4.428571429 + t = -4.280949733 Solving -4.428571429 + t = -4.280949733 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.428571429' to each side of the equation. -4.428571429 + 4.428571429 + t = -4.280949733 + 4.428571429 Combine like terms: -4.428571429 + 4.428571429 = 0.000000000 0.000000000 + t = -4.280949733 + 4.428571429 t = -4.280949733 + 4.428571429 Combine like terms: -4.280949733 + 4.428571429 = 0.147621696 t = 0.147621696 Simplifying t = 0.147621696Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.709521162, 0.147621696}
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