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Simplifying -2x + -3x(6x + -11) = -7 Reorder the terms: -2x + -3x(-11 + 6x) = -7 -2x + (-11 * -3x + 6x * -3x) = -7 -2x + (33x + -18x2) = -7 Combine like terms: -2x + 33x = 31x 31x + -18x2 = -7 Solving 31x + -18x2 = -7 Solving for variable 'x'. Reorder the terms: 7 + 31x + -18x2 = -7 + 7 Combine like terms: -7 + 7 = 0 7 + 31x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.3888888889 + -1.722222222x + x2 = 0 Move the constant term to the right: Add '0.3888888889' to each side of the equation. -0.3888888889 + -1.722222222x + 0.3888888889 + x2 = 0 + 0.3888888889 Reorder the terms: -0.3888888889 + 0.3888888889 + -1.722222222x + x2 = 0 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + -1.722222222x + x2 = 0 + 0.3888888889 -1.722222222x + x2 = 0 + 0.3888888889 Combine like terms: 0 + 0.3888888889 = 0.3888888889 -1.722222222x + x2 = 0.3888888889 The x term is -1.722222222x. Take half its coefficient (-0.861111111). Square it (0.7415123455) and add it to both sides. Add '0.7415123455' to each side of the equation. -1.722222222x + 0.7415123455 + x2 = 0.3888888889 + 0.7415123455 Reorder the terms: 0.7415123455 + -1.722222222x + x2 = 0.3888888889 + 0.7415123455 Combine like terms: 0.3888888889 + 0.7415123455 = 1.1304012344 0.7415123455 + -1.722222222x + x2 = 1.1304012344 Factor a perfect square on the left side: (x + -0.861111111)(x + -0.861111111) = 1.1304012344 Calculate the square root of the right side: 1.063203289 Break this problem into two subproblems by setting (x + -0.861111111) equal to 1.063203289 and -1.063203289.Subproblem 1
x + -0.861111111 = 1.063203289 Simplifying x + -0.861111111 = 1.063203289 Reorder the terms: -0.861111111 + x = 1.063203289 Solving -0.861111111 + x = 1.063203289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.861111111' to each side of the equation. -0.861111111 + 0.861111111 + x = 1.063203289 + 0.861111111 Combine like terms: -0.861111111 + 0.861111111 = 0.000000000 0.000000000 + x = 1.063203289 + 0.861111111 x = 1.063203289 + 0.861111111 Combine like terms: 1.063203289 + 0.861111111 = 1.9243144 x = 1.9243144 Simplifying x = 1.9243144Subproblem 2
x + -0.861111111 = -1.063203289 Simplifying x + -0.861111111 = -1.063203289 Reorder the terms: -0.861111111 + x = -1.063203289 Solving -0.861111111 + x = -1.063203289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.861111111' to each side of the equation. -0.861111111 + 0.861111111 + x = -1.063203289 + 0.861111111 Combine like terms: -0.861111111 + 0.861111111 = 0.000000000 0.000000000 + x = -1.063203289 + 0.861111111 x = -1.063203289 + 0.861111111 Combine like terms: -1.063203289 + 0.861111111 = -0.202092178 x = -0.202092178 Simplifying x = -0.202092178Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9243144, -0.202092178}
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