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Simplifying 0.29x2 + -4x = -8 Reorder the terms: -4x + 0.29x2 = -8 Solving -4x + 0.29x2 = -8 Solving for variable 'x'. Reorder the terms: 8 + -4x + 0.29x2 = -8 + 8 Combine like terms: -8 + 8 = 0 8 + -4x + 0.29x2 = 0 Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. 27.5862069 + -13.79310345x + x2 = 0 Move the constant term to the right: Add '-27.5862069' to each side of the equation. 27.5862069 + -13.79310345x + -27.5862069 + x2 = 0 + -27.5862069 Reorder the terms: 27.5862069 + -27.5862069 + -13.79310345x + x2 = 0 + -27.5862069 Combine like terms: 27.5862069 + -27.5862069 = 0.0000000 0.0000000 + -13.79310345x + x2 = 0 + -27.5862069 -13.79310345x + x2 = 0 + -27.5862069 Combine like terms: 0 + -27.5862069 = -27.5862069 -13.79310345x + x2 = -27.5862069 The x term is -13.79310345x. Take half its coefficient (-6.896551725). Square it (47.56242570) and add it to both sides. Add '47.56242570' to each side of the equation. -13.79310345x + 47.56242570 + x2 = -27.5862069 + 47.56242570 Reorder the terms: 47.56242570 + -13.79310345x + x2 = -27.5862069 + 47.56242570 Combine like terms: -27.5862069 + 47.56242570 = 19.9762188 47.56242570 + -13.79310345x + x2 = 19.9762188 Factor a perfect square on the left side: (x + -6.896551725)(x + -6.896551725) = 19.9762188 Calculate the square root of the right side: 4.469476345 Break this problem into two subproblems by setting (x + -6.896551725) equal to 4.469476345 and -4.469476345.Subproblem 1
x + -6.896551725 = 4.469476345 Simplifying x + -6.896551725 = 4.469476345 Reorder the terms: -6.896551725 + x = 4.469476345 Solving -6.896551725 + x = 4.469476345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.896551725' to each side of the equation. -6.896551725 + 6.896551725 + x = 4.469476345 + 6.896551725 Combine like terms: -6.896551725 + 6.896551725 = 0.000000000 0.000000000 + x = 4.469476345 + 6.896551725 x = 4.469476345 + 6.896551725 Combine like terms: 4.469476345 + 6.896551725 = 11.36602807 x = 11.36602807 Simplifying x = 11.36602807Subproblem 2
x + -6.896551725 = -4.469476345 Simplifying x + -6.896551725 = -4.469476345 Reorder the terms: -6.896551725 + x = -4.469476345 Solving -6.896551725 + x = -4.469476345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.896551725' to each side of the equation. -6.896551725 + 6.896551725 + x = -4.469476345 + 6.896551725 Combine like terms: -6.896551725 + 6.896551725 = 0.000000000 0.000000000 + x = -4.469476345 + 6.896551725 x = -4.469476345 + 6.896551725 Combine like terms: -4.469476345 + 6.896551725 = 2.42707538 x = 2.42707538 Simplifying x = 2.42707538Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.36602807, 2.42707538}
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