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Simplifying 18x2 + -4x = 46 Reorder the terms: -4x + 18x2 = 46 Solving -4x + 18x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + -4x + 18x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -4x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-23 + -2x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-23 + -2x + 9x2)' equal to zero and attempt to solve: Simplifying -23 + -2x + 9x2 = 0 Solving -23 + -2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.555555556 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '2.555555556' to each side of the equation. -2.555555556 + -0.2222222222x + 2.555555556 + x2 = 0 + 2.555555556 Reorder the terms: -2.555555556 + 2.555555556 + -0.2222222222x + x2 = 0 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 2.555555556 -0.2222222222x + x2 = 0 + 2.555555556 Combine like terms: 0 + 2.555555556 = 2.555555556 -0.2222222222x + x2 = 2.555555556 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 = 2.555555556 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 2.555555556 + 0.01234567901 Combine like terms: 2.555555556 + 0.01234567901 = 2.56790123501 0.01234567901 + -0.2222222222x + x2 = 2.56790123501 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 2.56790123501 Calculate the square root of the right side: 1.602467234 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.602467234 and -1.602467234.Subproblem 1
x + -0.1111111111 = 1.602467234 Simplifying x + -0.1111111111 = 1.602467234 Reorder the terms: -0.1111111111 + x = 1.602467234 Solving -0.1111111111 + x = 1.602467234 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 = 1.602467234 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.602467234 + 0.1111111111 x = 1.602467234 + 0.1111111111 Combine like terms: 1.602467234 + 0.1111111111 = 1.7135783451 x = 1.7135783451 Simplifying x = 1.7135783451Subproblem 2
x + -0.1111111111 = -1.602467234 Simplifying x + -0.1111111111 = -1.602467234 Reorder the terms: -0.1111111111 + x = -1.602467234 Solving -0.1111111111 + x = -1.602467234 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 = -1.602467234 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.602467234 + 0.1111111111 x = -1.602467234 + 0.1111111111 Combine like terms: -1.602467234 + 0.1111111111 = -1.4913561229 x = -1.4913561229 Simplifying x = -1.4913561229Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.7135783451, -1.4913561229}Solution
x = {1.7135783451, -1.4913561229}
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