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Simplifying x2 + -40x + 14 = 0 Reorder the terms: 14 + -40x + x2 = 0 Solving 14 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -40x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -40x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -40x + x2 = 0 + -14 -40x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -40x + x2 = -14 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -14 + 400 Reorder the terms: 400 + -40x + x2 = -14 + 400 Combine like terms: -14 + 400 = 386 400 + -40x + x2 = 386 Factor a perfect square on the left side: (x + -20)(x + -20) = 386 Calculate the square root of the right side: 19.646882704 Break this problem into two subproblems by setting (x + -20) equal to 19.646882704 and -19.646882704.Subproblem 1
x + -20 = 19.646882704 Simplifying x + -20 = 19.646882704 Reorder the terms: -20 + x = 19.646882704 Solving -20 + x = 19.646882704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.646882704 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.646882704 + 20 x = 19.646882704 + 20 Combine like terms: 19.646882704 + 20 = 39.646882704 x = 39.646882704 Simplifying x = 39.646882704Subproblem 2
x + -20 = -19.646882704 Simplifying x + -20 = -19.646882704 Reorder the terms: -20 + x = -19.646882704 Solving -20 + x = -19.646882704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.646882704 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.646882704 + 20 x = -19.646882704 + 20 Combine like terms: -19.646882704 + 20 = 0.353117296 x = 0.353117296 Simplifying x = 0.353117296Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.646882704, 0.353117296}
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