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Simplifying 18x2 + -1x + -2 = 0 Reorder the terms: -2 + -1x + 18x2 = 0 Solving -2 + -1x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.1111111111 + -0.05555555556x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.05555555556x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.05555555556x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.05555555556x + x2 = 0 + 0.1111111111 -0.05555555556x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.05555555556x + x2 = 0.1111111111 The x term is -0.05555555556x. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556x + 0.0007716049384 + x2 = 0.1111111111 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556x + x2 = 0.1111111111 + 0.0007716049384 Combine like terms: 0.1111111111 + 0.0007716049384 = 0.1118827160384 0.0007716049384 + -0.05555555556x + x2 = 0.1118827160384 Factor a perfect square on the left side: (x + -0.02777777778)(x + -0.02777777778) = 0.1118827160384 Calculate the square root of the right side: 0.334488738 Break this problem into two subproblems by setting (x + -0.02777777778) equal to 0.334488738 and -0.334488738.Subproblem 1
x + -0.02777777778 = 0.334488738 Simplifying x + -0.02777777778 = 0.334488738 Reorder the terms: -0.02777777778 + x = 0.334488738 Solving -0.02777777778 + x = 0.334488738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = 0.334488738 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = 0.334488738 + 0.02777777778 x = 0.334488738 + 0.02777777778 Combine like terms: 0.334488738 + 0.02777777778 = 0.36226651578 x = 0.36226651578 Simplifying x = 0.36226651578Subproblem 2
x + -0.02777777778 = -0.334488738 Simplifying x + -0.02777777778 = -0.334488738 Reorder the terms: -0.02777777778 + x = -0.334488738 Solving -0.02777777778 + x = -0.334488738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = -0.334488738 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = -0.334488738 + 0.02777777778 x = -0.334488738 + 0.02777777778 Combine like terms: -0.334488738 + 0.02777777778 = -0.30671096022 x = -0.30671096022 Simplifying x = -0.30671096022Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.36226651578, -0.30671096022}
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