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Simplifying 54x2 + 57x + -3 = 0 Reorder the terms: -3 + 57x + 54x2 = 0 Solving -3 + 57x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 19x + 18x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 19x + 18x2)' equal to zero and attempt to solve: Simplifying -1 + 19x + 18x2 = 0 Solving -1 + 19x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.05555555556 + 1.055555556x + x2 = 0 Move the constant term to the right: Add '0.05555555556' to each side of the equation. -0.05555555556 + 1.055555556x + 0.05555555556 + x2 = 0 + 0.05555555556 Reorder the terms: -0.05555555556 + 0.05555555556 + 1.055555556x + x2 = 0 + 0.05555555556 Combine like terms: -0.05555555556 + 0.05555555556 = 0.00000000000 0.00000000000 + 1.055555556x + x2 = 0 + 0.05555555556 1.055555556x + x2 = 0 + 0.05555555556 Combine like terms: 0 + 0.05555555556 = 0.05555555556 1.055555556x + x2 = 0.05555555556 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 = 0.05555555556 + 0.2785493830 Reorder the terms: 0.2785493830 + 1.055555556x + x2 = 0.05555555556 + 0.2785493830 Combine like terms: 0.05555555556 + 0.2785493830 = 0.33410493856 0.2785493830 + 1.055555556x + x2 = 0.33410493856 Factor a perfect square on the left side: (x + 0.527777778)(x + 0.527777778) = 0.33410493856 Calculate the square root of the right side: 0.578018113 Break this problem into two subproblems by setting (x + 0.527777778) equal to 0.578018113 and -0.578018113.Subproblem 1
x + 0.527777778 = 0.578018113 Simplifying x + 0.527777778 = 0.578018113 Reorder the terms: 0.527777778 + x = 0.578018113 Solving 0.527777778 + x = 0.578018113 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 = 0.578018113 + -0.527777778 Combine like terms: 0.527777778 + -0.527777778 = 0.000000000 0.000000000 + x = 0.578018113 + -0.527777778 x = 0.578018113 + -0.527777778 Combine like terms: 0.578018113 + -0.527777778 = 0.050240335 x = 0.050240335 Simplifying x = 0.050240335Subproblem 2
x + 0.527777778 = -0.578018113 Simplifying x + 0.527777778 = -0.578018113 Reorder the terms: 0.527777778 + x = -0.578018113 Solving 0.527777778 + x = -0.578018113 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 = -0.578018113 + -0.527777778 Combine like terms: 0.527777778 + -0.527777778 = 0.000000000 0.000000000 + x = -0.578018113 + -0.527777778 x = -0.578018113 + -0.527777778 Combine like terms: -0.578018113 + -0.527777778 = -1.105795891 x = -1.105795891 Simplifying x = -1.105795891Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.050240335, -1.105795891}Solution
x = {0.050240335, -1.105795891}
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