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Simplifying 3x2 + -7x + -27 = 0 Reorder the terms: -27 + -7x + 3x2 = 0 Solving -27 + -7x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -9 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.333333333x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.333333333x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.333333333x + x2 = 0 + 9 -2.333333333x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.333333333x + x2 = 9 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = 9 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = 9 + 1.361111112 Combine like terms: 9 + 1.361111112 = 10.361111112 1.361111112 + -2.333333333x + x2 = 10.361111112 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 10.361111112 Calculate the square root of the right side: 3.218867986 Break this problem into two subproblems by setting (x + -1.166666667) equal to 3.218867986 and -3.218867986.Subproblem 1
x + -1.166666667 = 3.218867986 Simplifying x + -1.166666667 = 3.218867986 Reorder the terms: -1.166666667 + x = 3.218867986 Solving -1.166666667 + x = 3.218867986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 3.218867986 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 3.218867986 + 1.166666667 x = 3.218867986 + 1.166666667 Combine like terms: 3.218867986 + 1.166666667 = 4.385534653 x = 4.385534653 Simplifying x = 4.385534653Subproblem 2
x + -1.166666667 = -3.218867986 Simplifying x + -1.166666667 = -3.218867986 Reorder the terms: -1.166666667 + x = -3.218867986 Solving -1.166666667 + x = -3.218867986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -3.218867986 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -3.218867986 + 1.166666667 x = -3.218867986 + 1.166666667 Combine like terms: -3.218867986 + 1.166666667 = -2.052201319 x = -2.052201319 Simplifying x = -2.052201319Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.385534653, -2.052201319}
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