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Simplifying -2.29t + 4.9t2 + -22 = 0 Reorder the terms: -22 + -2.29t + 4.9t2 = 0 Solving -22 + -2.29t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.489795918 + -0.4673469388t + t2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + -0.4673469388t + 4.489795918 + t2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + -0.4673469388t + t2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + -0.4673469388t + t2 = 0 + 4.489795918 -0.4673469388t + t2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 -0.4673469388t + t2 = 4.489795918 The t term is -0.4673469388t. Take half its coefficient (-0.2336734694). Square it (0.05460329030) and add it to both sides. Add '0.05460329030' to each side of the equation. -0.4673469388t + 0.05460329030 + t2 = 4.489795918 + 0.05460329030 Reorder the terms: 0.05460329030 + -0.4673469388t + t2 = 4.489795918 + 0.05460329030 Combine like terms: 4.489795918 + 0.05460329030 = 4.5443992083 0.05460329030 + -0.4673469388t + t2 = 4.5443992083 Factor a perfect square on the left side: (t + -0.2336734694)(t + -0.2336734694) = 4.5443992083 Calculate the square root of the right side: 2.131759651 Break this problem into two subproblems by setting (t + -0.2336734694) equal to 2.131759651 and -2.131759651.Subproblem 1
t + -0.2336734694 = 2.131759651 Simplifying t + -0.2336734694 = 2.131759651 Reorder the terms: -0.2336734694 + t = 2.131759651 Solving -0.2336734694 + t = 2.131759651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2336734694' to each side of the equation. -0.2336734694 + 0.2336734694 + t = 2.131759651 + 0.2336734694 Combine like terms: -0.2336734694 + 0.2336734694 = 0.0000000000 0.0000000000 + t = 2.131759651 + 0.2336734694 t = 2.131759651 + 0.2336734694 Combine like terms: 2.131759651 + 0.2336734694 = 2.3654331204 t = 2.3654331204 Simplifying t = 2.3654331204Subproblem 2
t + -0.2336734694 = -2.131759651 Simplifying t + -0.2336734694 = -2.131759651 Reorder the terms: -0.2336734694 + t = -2.131759651 Solving -0.2336734694 + t = -2.131759651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2336734694' to each side of the equation. -0.2336734694 + 0.2336734694 + t = -2.131759651 + 0.2336734694 Combine like terms: -0.2336734694 + 0.2336734694 = 0.0000000000 0.0000000000 + t = -2.131759651 + 0.2336734694 t = -2.131759651 + 0.2336734694 Combine like terms: -2.131759651 + 0.2336734694 = -1.8980861816 t = -1.8980861816 Simplifying t = -1.8980861816Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.3654331204, -1.8980861816}
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