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Simplifying 18x2 + 19x + -5 = 0 Reorder the terms: -5 + 19x + 18x2 = 0 Solving -5 + 19x + 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 + 1.055555556x + x2 = 0 Move the constant term to the right: Add '0.2777777778' to each side of the equation. -0.2777777778 + 1.055555556x + 0.2777777778 + x2 = 0 + 0.2777777778 Reorder the terms: -0.2777777778 + 0.2777777778 + 1.055555556x + x2 = 0 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + 1.055555556x + x2 = 0 + 0.2777777778 1.055555556x + x2 = 0 + 0.2777777778 Combine like terms: 0 + 0.2777777778 = 0.2777777778 1.055555556x + x2 = 0.2777777778 The x term is 1.055555556x. Take half its coefficient (0.527777778). Square it (0.2785493830) and add it to both sides. Add '0.2785493830' to each side of the equation. 1.055555556x + 0.2785493830 + x2 = 0.2777777778 + 0.2785493830 Reorder the terms: 0.2785493830 + 1.055555556x + x2 = 0.2777777778 + 0.2785493830 Combine like terms: 0.2777777778 + 0.2785493830 = 0.5563271608 0.2785493830 + 1.055555556x + x2 = 0.5563271608 Factor a perfect square on the left side: (x + 0.527777778)(x + 0.527777778) = 0.5563271608 Calculate the square root of the right side: 0.745873421 Break this problem into two subproblems by setting (x + 0.527777778) equal to 0.745873421 and -0.745873421.Subproblem 1
x + 0.527777778 = 0.745873421 Simplifying x + 0.527777778 = 0.745873421 Reorder the terms: 0.527777778 + x = 0.745873421 Solving 0.527777778 + x = 0.745873421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.527777778' to each side of the equation. 0.527777778 + -0.527777778 + x = 0.745873421 + -0.527777778 Combine like terms: 0.527777778 + -0.527777778 = 0.000000000 0.000000000 + x = 0.745873421 + -0.527777778 x = 0.745873421 + -0.527777778 Combine like terms: 0.745873421 + -0.527777778 = 0.218095643 x = 0.218095643 Simplifying x = 0.218095643Subproblem 2
x + 0.527777778 = -0.745873421 Simplifying x + 0.527777778 = -0.745873421 Reorder the terms: 0.527777778 + x = -0.745873421 Solving 0.527777778 + x = -0.745873421 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.527777778' to each side of the equation. 0.527777778 + -0.527777778 + x = -0.745873421 + -0.527777778 Combine like terms: 0.527777778 + -0.527777778 = 0.000000000 0.000000000 + x = -0.745873421 + -0.527777778 x = -0.745873421 + -0.527777778 Combine like terms: -0.745873421 + -0.527777778 = -1.273651199 x = -1.273651199 Simplifying x = -1.273651199Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.218095643, -1.273651199}
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