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Simplifying 356x = 2 + 4x2 Solving 356x = 2 + 4x2 Solving for variable 'x'. Reorder the terms: -2 + 356x + -4x2 = 2 + 4x2 + -2 + -4x2 Reorder the terms: -2 + 356x + -4x2 = 2 + -2 + 4x2 + -4x2 Combine like terms: 2 + -2 = 0 -2 + 356x + -4x2 = 0 + 4x2 + -4x2 -2 + 356x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -2 + 356x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 178x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 178x + -2x2)' equal to zero and attempt to solve: Simplifying -1 + 178x + -2x2 = 0 Solving -1 + 178x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -89x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -89x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -89x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -89x + x2 = 0 + -0.5 -89x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -89x + x2 = -0.5 The x term is -89x. Take half its coefficient (-44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. -89x + 1980.25 + x2 = -0.5 + 1980.25 Reorder the terms: 1980.25 + -89x + x2 = -0.5 + 1980.25 Combine like terms: -0.5 + 1980.25 = 1979.75 1980.25 + -89x + x2 = 1979.75 Factor a perfect square on the left side: (x + -44.5)(x + -44.5) = 1979.75 Calculate the square root of the right side: 44.494381668 Break this problem into two subproblems by setting (x + -44.5) equal to 44.494381668 and -44.494381668.Subproblem 1
x + -44.5 = 44.494381668 Simplifying x + -44.5 = 44.494381668 Reorder the terms: -44.5 + x = 44.494381668 Solving -44.5 + x = 44.494381668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = 44.494381668 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = 44.494381668 + 44.5 x = 44.494381668 + 44.5 Combine like terms: 44.494381668 + 44.5 = 88.994381668 x = 88.994381668 Simplifying x = 88.994381668Subproblem 2
x + -44.5 = -44.494381668 Simplifying x + -44.5 = -44.494381668 Reorder the terms: -44.5 + x = -44.494381668 Solving -44.5 + x = -44.494381668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = -44.494381668 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = -44.494381668 + 44.5 x = -44.494381668 + 44.5 Combine like terms: -44.494381668 + 44.5 = 0.005618332 x = 0.005618332 Simplifying x = 0.005618332Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.994381668, 0.005618332}Solution
x = {88.994381668, 0.005618332}
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