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Simplifying 18x2 = 4x + 23 Reorder the terms: 18x2 = 23 + 4x Solving 18x2 = 23 + 4x Solving for variable 'x'. Reorder the terms: -23 + -4x + 18x2 = 23 + 4x + -23 + -4x Reorder the terms: -23 + -4x + 18x2 = 23 + -23 + 4x + -4x Combine like terms: 23 + -23 = 0 -23 + -4x + 18x2 = 0 + 4x + -4x -23 + -4x + 18x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -23 + -4x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -1.277777778 + -0.2222222222x + x2 = 0 Move the constant term to the right: Add '1.277777778' to each side of the equation. -1.277777778 + -0.2222222222x + 1.277777778 + x2 = 0 + 1.277777778 Reorder the terms: -1.277777778 + 1.277777778 + -0.2222222222x + x2 = 0 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + -0.2222222222x + x2 = 0 + 1.277777778 -0.2222222222x + x2 = 0 + 1.277777778 Combine like terms: 0 + 1.277777778 = 1.277777778 -0.2222222222x + x2 = 1.277777778 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 = 1.277777778 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222x + x2 = 1.277777778 + 0.01234567901 Combine like terms: 1.277777778 + 0.01234567901 = 1.29012345701 0.01234567901 + -0.2222222222x + x2 = 1.29012345701 Factor a perfect square on the left side: (x + -0.1111111111)(x + -0.1111111111) = 1.29012345701 Calculate the square root of the right side: 1.135836017 Break this problem into two subproblems by setting (x + -0.1111111111) equal to 1.135836017 and -1.135836017.Subproblem 1
x + -0.1111111111 = 1.135836017 Simplifying x + -0.1111111111 = 1.135836017 Reorder the terms: -0.1111111111 + x = 1.135836017 Solving -0.1111111111 + x = 1.135836017 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 = 1.135836017 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 1.135836017 + 0.1111111111 x = 1.135836017 + 0.1111111111 Combine like terms: 1.135836017 + 0.1111111111 = 1.2469471281 x = 1.2469471281 Simplifying x = 1.2469471281Subproblem 2
x + -0.1111111111 = -1.135836017 Simplifying x + -0.1111111111 = -1.135836017 Reorder the terms: -0.1111111111 + x = -1.135836017 Solving -0.1111111111 + x = -1.135836017 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 = -1.135836017 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -1.135836017 + 0.1111111111 x = -1.135836017 + 0.1111111111 Combine like terms: -1.135836017 + 0.1111111111 = -1.0247249059 x = -1.0247249059 Simplifying x = -1.0247249059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2469471281, -1.0247249059}
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