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Simplifying 18x2 + -55x + 5 = 0 Reorder the terms: 5 + -55x + 18x2 = 0 Solving 5 + -55x + 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'. 0.2777777778 + -3.055555556x + x2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + -3.055555556x + -0.2777777778 + x2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + -3.055555556x + x2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + -3.055555556x + x2 = 0 + -0.2777777778 -3.055555556x + x2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 -3.055555556x + x2 = -0.2777777778 The x term is -3.055555556x. Take half its coefficient (-1.527777778). Square it (2.334104939) and add it to both sides. Add '2.334104939' to each side of the equation. -3.055555556x + 2.334104939 + x2 = -0.2777777778 + 2.334104939 Reorder the terms: 2.334104939 + -3.055555556x + x2 = -0.2777777778 + 2.334104939 Combine like terms: -0.2777777778 + 2.334104939 = 2.0563271612 2.334104939 + -3.055555556x + x2 = 2.0563271612 Factor a perfect square on the left side: (x + -1.527777778)(x + -1.527777778) = 2.0563271612 Calculate the square root of the right side: 1.433989945 Break this problem into two subproblems by setting (x + -1.527777778) equal to 1.433989945 and -1.433989945.Subproblem 1
x + -1.527777778 = 1.433989945 Simplifying x + -1.527777778 = 1.433989945 Reorder the terms: -1.527777778 + x = 1.433989945 Solving -1.527777778 + x = 1.433989945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.527777778' to each side of the equation. -1.527777778 + 1.527777778 + x = 1.433989945 + 1.527777778 Combine like terms: -1.527777778 + 1.527777778 = 0.000000000 0.000000000 + x = 1.433989945 + 1.527777778 x = 1.433989945 + 1.527777778 Combine like terms: 1.433989945 + 1.527777778 = 2.961767723 x = 2.961767723 Simplifying x = 2.961767723Subproblem 2
x + -1.527777778 = -1.433989945 Simplifying x + -1.527777778 = -1.433989945 Reorder the terms: -1.527777778 + x = -1.433989945 Solving -1.527777778 + x = -1.433989945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.527777778' to each side of the equation. -1.527777778 + 1.527777778 + x = -1.433989945 + 1.527777778 Combine like terms: -1.527777778 + 1.527777778 = 0.000000000 0.000000000 + x = -1.433989945 + 1.527777778 x = -1.433989945 + 1.527777778 Combine like terms: -1.433989945 + 1.527777778 = 0.093787833 x = 0.093787833 Simplifying x = 0.093787833Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.961767723, 0.093787833}
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