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Simplifying 5.5x2 + -19.5x + 13 = 0 Reorder the terms: 13 + -19.5x + 5.5x2 = 0 Solving 13 + -19.5x + 5.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.5 the coefficient of the squared term: Divide each side by '5.5'. 2.363636364 + -3.545454545x + x2 = 0 Move the constant term to the right: Add '-2.363636364' to each side of the equation. 2.363636364 + -3.545454545x + -2.363636364 + x2 = 0 + -2.363636364 Reorder the terms: 2.363636364 + -2.363636364 + -3.545454545x + x2 = 0 + -2.363636364 Combine like terms: 2.363636364 + -2.363636364 = 0.000000000 0.000000000 + -3.545454545x + x2 = 0 + -2.363636364 -3.545454545x + x2 = 0 + -2.363636364 Combine like terms: 0 + -2.363636364 = -2.363636364 -3.545454545x + x2 = -2.363636364 The x term is -3.545454545x. Take half its coefficient (-1.772727273). Square it (3.142561984) and add it to both sides. Add '3.142561984' to each side of the equation. -3.545454545x + 3.142561984 + x2 = -2.363636364 + 3.142561984 Reorder the terms: 3.142561984 + -3.545454545x + x2 = -2.363636364 + 3.142561984 Combine like terms: -2.363636364 + 3.142561984 = 0.77892562 3.142561984 + -3.545454545x + x2 = 0.77892562 Factor a perfect square on the left side: (x + -1.772727273)(x + -1.772727273) = 0.77892562 Calculate the square root of the right side: 0.882567629 Break this problem into two subproblems by setting (x + -1.772727273) equal to 0.882567629 and -0.882567629.Subproblem 1
x + -1.772727273 = 0.882567629 Simplifying x + -1.772727273 = 0.882567629 Reorder the terms: -1.772727273 + x = 0.882567629 Solving -1.772727273 + x = 0.882567629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.772727273' to each side of the equation. -1.772727273 + 1.772727273 + x = 0.882567629 + 1.772727273 Combine like terms: -1.772727273 + 1.772727273 = 0.000000000 0.000000000 + x = 0.882567629 + 1.772727273 x = 0.882567629 + 1.772727273 Combine like terms: 0.882567629 + 1.772727273 = 2.655294902 x = 2.655294902 Simplifying x = 2.655294902Subproblem 2
x + -1.772727273 = -0.882567629 Simplifying x + -1.772727273 = -0.882567629 Reorder the terms: -1.772727273 + x = -0.882567629 Solving -1.772727273 + x = -0.882567629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.772727273' to each side of the equation. -1.772727273 + 1.772727273 + x = -0.882567629 + 1.772727273 Combine like terms: -1.772727273 + 1.772727273 = 0.000000000 0.000000000 + x = -0.882567629 + 1.772727273 x = -0.882567629 + 1.772727273 Combine like terms: -0.882567629 + 1.772727273 = 0.890159644 x = 0.890159644 Simplifying x = 0.890159644Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.655294902, 0.890159644}
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