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Simplifying 160 = 17t2 + -130t Reorder the terms: 160 = -130t + 17t2 Solving 160 = -130t + 17t2 Solving for variable 't'. Reorder the terms: 160 + 130t + -17t2 = -130t + 130t + 17t2 + -17t2 Combine like terms: -130t + 130t = 0 160 + 130t + -17t2 = 0 + 17t2 + -17t2 160 + 130t + -17t2 = 17t2 + -17t2 Combine like terms: 17t2 + -17t2 = 0 160 + 130t + -17t2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -9.411764706 + -7.647058824t + t2 = 0 Move the constant term to the right: Add '9.411764706' to each side of the equation. -9.411764706 + -7.647058824t + 9.411764706 + t2 = 0 + 9.411764706 Reorder the terms: -9.411764706 + 9.411764706 + -7.647058824t + t2 = 0 + 9.411764706 Combine like terms: -9.411764706 + 9.411764706 = 0.000000000 0.000000000 + -7.647058824t + t2 = 0 + 9.411764706 -7.647058824t + t2 = 0 + 9.411764706 Combine like terms: 0 + 9.411764706 = 9.411764706 -7.647058824t + t2 = 9.411764706 The t term is -7.647058824t. Take half its coefficient (-3.823529412). Square it (14.61937716) and add it to both sides. Add '14.61937716' to each side of the equation. -7.647058824t + 14.61937716 + t2 = 9.411764706 + 14.61937716 Reorder the terms: 14.61937716 + -7.647058824t + t2 = 9.411764706 + 14.61937716 Combine like terms: 9.411764706 + 14.61937716 = 24.031141866 14.61937716 + -7.647058824t + t2 = 24.031141866 Factor a perfect square on the left side: (t + -3.823529412)(t + -3.823529412) = 24.031141866 Calculate the square root of the right side: 4.902156859 Break this problem into two subproblems by setting (t + -3.823529412) equal to 4.902156859 and -4.902156859.Subproblem 1
t + -3.823529412 = 4.902156859 Simplifying t + -3.823529412 = 4.902156859 Reorder the terms: -3.823529412 + t = 4.902156859 Solving -3.823529412 + t = 4.902156859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.823529412' to each side of the equation. -3.823529412 + 3.823529412 + t = 4.902156859 + 3.823529412 Combine like terms: -3.823529412 + 3.823529412 = 0.000000000 0.000000000 + t = 4.902156859 + 3.823529412 t = 4.902156859 + 3.823529412 Combine like terms: 4.902156859 + 3.823529412 = 8.725686271 t = 8.725686271 Simplifying t = 8.725686271Subproblem 2
t + -3.823529412 = -4.902156859 Simplifying t + -3.823529412 = -4.902156859 Reorder the terms: -3.823529412 + t = -4.902156859 Solving -3.823529412 + t = -4.902156859 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.823529412' to each side of the equation. -3.823529412 + 3.823529412 + t = -4.902156859 + 3.823529412 Combine like terms: -3.823529412 + 3.823529412 = 0.000000000 0.000000000 + t = -4.902156859 + 3.823529412 t = -4.902156859 + 3.823529412 Combine like terms: -4.902156859 + 3.823529412 = -1.078627447 t = -1.078627447 Simplifying t = -1.078627447Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.725686271, -1.078627447}
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