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Simplifying -4x = -18 + 9x2 + -6x Reorder the terms: -4x = -18 + -6x + 9x2 Solving -4x = -18 + -6x + 9x2 Solving for variable 'x'. Reorder the terms: 18 + -4x + 6x + -9x2 = -18 + -6x + 9x2 + 18 + 6x + -9x2 Combine like terms: -4x + 6x = 2x 18 + 2x + -9x2 = -18 + -6x + 9x2 + 18 + 6x + -9x2 Reorder the terms: 18 + 2x + -9x2 = -18 + 18 + -6x + 6x + 9x2 + -9x2 Combine like terms: -18 + 18 = 0 18 + 2x + -9x2 = 0 + -6x + 6x + 9x2 + -9x2 18 + 2x + -9x2 = -6x + 6x + 9x2 + -9x2 Combine like terms: -6x + 6x = 0 18 + 2x + -9x2 = 0 + 9x2 + -9x2 18 + 2x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 18 + 2x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -2 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.2222222222x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.2222222222x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.2222222222x + x2 = 0 + 2 -0.2222222222x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.2222222222x + x2 = 2 The x term is -0.2222222222x. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222x + 0.01234567901 + x2 = 2 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 2 + 0.01234567901 Combine like terms: 2 + 0.01234567901 = 2.01234567901 0.01234567901 + -0.2222222222x + x2 = 2.01234567901 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 2.01234567901 Calculate the square root of the right side: 1.418571704 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.418571704 and -1.418571704.Subproblem 1
x + -0.1111111111 = 1.418571704 Simplifying x + -0.1111111111 = 1.418571704 Reorder the terms: -0.1111111111 + x = 1.418571704 Solving -0.1111111111 + x = 1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 1.418571704 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.418571704 + 0.1111111111 x = 1.418571704 + 0.1111111111 Combine like terms: 1.418571704 + 0.1111111111 = 1.5296828151 x = 1.5296828151 Simplifying x = 1.5296828151Subproblem 2
x + -0.1111111111 = -1.418571704 Simplifying x + -0.1111111111 = -1.418571704 Reorder the terms: -0.1111111111 + x = -1.418571704 Solving -0.1111111111 + x = -1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -1.418571704 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.418571704 + 0.1111111111 x = -1.418571704 + 0.1111111111 Combine like terms: -1.418571704 + 0.1111111111 = -1.3074605929 x = -1.3074605929 Simplifying x = -1.3074605929Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5296828151, -1.3074605929}
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