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Simplifying (0.9t + -0.7)(0.11t + 1) = 0 Reorder the terms: (-0.7 + 0.9t)(0.11t + 1) = 0 Reorder the terms: (-0.7 + 0.9t)(1 + 0.11t) = 0 Multiply (-0.7 + 0.9t) * (1 + 0.11t) (-0.7(1 + 0.11t) + 0.9t * (1 + 0.11t)) = 0 ((1 * -0.7 + 0.11t * -0.7) + 0.9t * (1 + 0.11t)) = 0 ((-0.7 + -0.077t) + 0.9t * (1 + 0.11t)) = 0 (-0.7 + -0.077t + (1 * 0.9t + 0.11t * 0.9t)) = 0 (-0.7 + -0.077t + (0.9t + 0.099t2)) = 0 Combine like terms: -0.077t + 0.9t = 0.823t (-0.7 + 0.823t + 0.099t2) = 0 Solving -0.7 + 0.823t + 0.099t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.099 the coefficient of the squared term: Divide each side by '0.099'. -7.070707071 + 8.313131313t + t2 = 0 Move the constant term to the right: Add '7.070707071' to each side of the equation. -7.070707071 + 8.313131313t + 7.070707071 + t2 = 0 + 7.070707071 Reorder the terms: -7.070707071 + 7.070707071 + 8.313131313t + t2 = 0 + 7.070707071 Combine like terms: -7.070707071 + 7.070707071 = 0.000000000 0.000000000 + 8.313131313t + t2 = 0 + 7.070707071 8.313131313t + t2 = 0 + 7.070707071 Combine like terms: 0 + 7.070707071 = 7.070707071 8.313131313t + t2 = 7.070707071 The t term is 8.313131313t. Take half its coefficient (4.156565657). Square it (17.27703806) and add it to both sides. Add '17.27703806' to each side of the equation. 8.313131313t + 17.27703806 + t2 = 7.070707071 + 17.27703806 Reorder the terms: 17.27703806 + 8.313131313t + t2 = 7.070707071 + 17.27703806 Combine like terms: 7.070707071 + 17.27703806 = 24.347745131 17.27703806 + 8.313131313t + t2 = 24.347745131 Factor a perfect square on the left side: (t + 4.156565657)(t + 4.156565657) = 24.347745131 Calculate the square root of the right side: 4.934343435 Break this problem into two subproblems by setting (t + 4.156565657) equal to 4.934343435 and -4.934343435.Subproblem 1
t + 4.156565657 = 4.934343435 Simplifying t + 4.156565657 = 4.934343435 Reorder the terms: 4.156565657 + t = 4.934343435 Solving 4.156565657 + t = 4.934343435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.156565657' to each side of the equation. 4.156565657 + -4.156565657 + t = 4.934343435 + -4.156565657 Combine like terms: 4.156565657 + -4.156565657 = 0.000000000 0.000000000 + t = 4.934343435 + -4.156565657 t = 4.934343435 + -4.156565657 Combine like terms: 4.934343435 + -4.156565657 = 0.777777778 t = 0.777777778 Simplifying t = 0.777777778Subproblem 2
t + 4.156565657 = -4.934343435 Simplifying t + 4.156565657 = -4.934343435 Reorder the terms: 4.156565657 + t = -4.934343435 Solving 4.156565657 + t = -4.934343435 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.156565657' to each side of the equation. 4.156565657 + -4.156565657 + t = -4.934343435 + -4.156565657 Combine like terms: 4.156565657 + -4.156565657 = 0.000000000 0.000000000 + t = -4.934343435 + -4.156565657 t = -4.934343435 + -4.156565657 Combine like terms: -4.934343435 + -4.156565657 = -9.090909092 t = -9.090909092 Simplifying t = -9.090909092Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.777777778, -9.090909092}
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