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Simplifying (4x + -2) * 4x + -2 + 5x(5x) = 0 Reorder the terms: (-2 + 4x) * 4x + -2 + 5x(5x) = 0 Reorder the terms for easier multiplication: 4x(-2 + 4x) + -2 + 5x(5x) = 0 (-2 * 4x + 4x * 4x) + -2 + 5x(5x) = 0 (-8x + 16x2) + -2 + 5x(5x) = 0 Remove parenthesis around (5x) -8x + 16x2 + -2 + 5x * 5x = 0 Reorder the terms for easier multiplication: -8x + 16x2 + -2 + 5 * 5x * x = 0 Multiply 5 * 5 -8x + 16x2 + -2 + 25x * x = 0 Multiply x * x -8x + 16x2 + -2 + 25x2 = 0 Reorder the terms: -2 + -8x + 16x2 + 25x2 = 0 Combine like terms: 16x2 + 25x2 = 41x2 -2 + -8x + 41x2 = 0 Solving -2 + -8x + 41x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 41 the coefficient of the squared term: Divide each side by '41'. -0.0487804878 + -0.1951219512x + x2 = 0 Move the constant term to the right: Add '0.0487804878' to each side of the equation. -0.0487804878 + -0.1951219512x + 0.0487804878 + x2 = 0 + 0.0487804878 Reorder the terms: -0.0487804878 + 0.0487804878 + -0.1951219512x + x2 = 0 + 0.0487804878 Combine like terms: -0.0487804878 + 0.0487804878 = 0.0000000000 0.0000000000 + -0.1951219512x + x2 = 0 + 0.0487804878 -0.1951219512x + x2 = 0 + 0.0487804878 Combine like terms: 0 + 0.0487804878 = 0.0487804878 -0.1951219512x + x2 = 0.0487804878 The x term is -0.1951219512x. Take half its coefficient (-0.0975609756). Square it (0.009518143960) and add it to both sides. Add '0.009518143960' to each side of the equation. -0.1951219512x + 0.009518143960 + x2 = 0.0487804878 + 0.009518143960 Reorder the terms: 0.009518143960 + -0.1951219512x + x2 = 0.0487804878 + 0.009518143960 Combine like terms: 0.0487804878 + 0.009518143960 = 0.05829863176 0.009518143960 + -0.1951219512x + x2 = 0.05829863176 Factor a perfect square on the left side: (x + -0.0975609756)(x + -0.0975609756) = 0.05829863176 Calculate the square root of the right side: 0.241451096 Break this problem into two subproblems by setting (x + -0.0975609756) equal to 0.241451096 and -0.241451096.Subproblem 1
x + -0.0975609756 = 0.241451096 Simplifying x + -0.0975609756 = 0.241451096 Reorder the terms: -0.0975609756 + x = 0.241451096 Solving -0.0975609756 + x = 0.241451096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0975609756' to each side of the equation. -0.0975609756 + 0.0975609756 + x = 0.241451096 + 0.0975609756 Combine like terms: -0.0975609756 + 0.0975609756 = 0.0000000000 0.0000000000 + x = 0.241451096 + 0.0975609756 x = 0.241451096 + 0.0975609756 Combine like terms: 0.241451096 + 0.0975609756 = 0.3390120716 x = 0.3390120716 Simplifying x = 0.3390120716Subproblem 2
x + -0.0975609756 = -0.241451096 Simplifying x + -0.0975609756 = -0.241451096 Reorder the terms: -0.0975609756 + x = -0.241451096 Solving -0.0975609756 + x = -0.241451096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0975609756' to each side of the equation. -0.0975609756 + 0.0975609756 + x = -0.241451096 + 0.0975609756 Combine like terms: -0.0975609756 + 0.0975609756 = 0.0000000000 0.0000000000 + x = -0.241451096 + 0.0975609756 x = -0.241451096 + 0.0975609756 Combine like terms: -0.241451096 + 0.0975609756 = -0.1438901204 x = -0.1438901204 Simplifying x = -0.1438901204Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3390120716, -0.1438901204}
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