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Simplifying 36x2 + 18x + 1 = 0 Reorder the terms: 1 + 18x + 36x2 = 0 Solving 1 + 18x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.02777777778 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.02777777778' to each side of the equation. 0.02777777778 + 0.5x + -0.02777777778 + x2 = 0 + -0.02777777778 Reorder the terms: 0.02777777778 + -0.02777777778 + 0.5x + x2 = 0 + -0.02777777778 Combine like terms: 0.02777777778 + -0.02777777778 = 0.00000000000 0.00000000000 + 0.5x + x2 = 0 + -0.02777777778 0.5x + x2 = 0 + -0.02777777778 Combine like terms: 0 + -0.02777777778 = -0.02777777778 0.5x + x2 = -0.02777777778 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = -0.02777777778 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.02777777778 + 0.0625 Combine like terms: -0.02777777778 + 0.0625 = 0.03472222222 0.0625 + 0.5x + x2 = 0.03472222222 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.03472222222 Calculate the square root of the right side: 0.186338998 Break this problem into two subproblems by setting (x + 0.25) equal to 0.186338998 and -0.186338998.Subproblem 1
x + 0.25 = 0.186338998 Simplifying x + 0.25 = 0.186338998 Reorder the terms: 0.25 + x = 0.186338998 Solving 0.25 + x = 0.186338998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.186338998 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.186338998 + -0.25 x = 0.186338998 + -0.25 Combine like terms: 0.186338998 + -0.25 = -0.063661002 x = -0.063661002 Simplifying x = -0.063661002Subproblem 2
x + 0.25 = -0.186338998 Simplifying x + 0.25 = -0.186338998 Reorder the terms: 0.25 + x = -0.186338998 Solving 0.25 + x = -0.186338998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.186338998 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.186338998 + -0.25 x = -0.186338998 + -0.25 Combine like terms: -0.186338998 + -0.25 = -0.436338998 x = -0.436338998 Simplifying x = -0.436338998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.063661002, -0.436338998}
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