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Simplifying x2 + -40x + 10 = 0 Reorder the terms: 10 + -40x + x2 = 0 Solving 10 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -40x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -40x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -40x + x2 = 0 + -10 -40x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -40x + x2 = -10 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 = -10 + 400 Reorder the terms: 400 + -40x + x2 = -10 + 400 Combine like terms: -10 + 400 = 390 400 + -40x + x2 = 390 Factor a perfect square on the left side: (x + -20)(x + -20) = 390 Calculate the square root of the right side: 19.748417658 Break this problem into two subproblems by setting (x + -20) equal to 19.748417658 and -19.748417658.Subproblem 1
x + -20 = 19.748417658 Simplifying x + -20 = 19.748417658 Reorder the terms: -20 + x = 19.748417658 Solving -20 + x = 19.748417658 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 = 19.748417658 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.748417658 + 20 x = 19.748417658 + 20 Combine like terms: 19.748417658 + 20 = 39.748417658 x = 39.748417658 Simplifying x = 39.748417658Subproblem 2
x + -20 = -19.748417658 Simplifying x + -20 = -19.748417658 Reorder the terms: -20 + x = -19.748417658 Solving -20 + x = -19.748417658 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 = -19.748417658 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.748417658 + 20 x = -19.748417658 + 20 Combine like terms: -19.748417658 + 20 = 0.251582342 x = 0.251582342 Simplifying x = 0.251582342Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.748417658, 0.251582342}
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