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Simplifying x2 + -40x + 383 = 0 Reorder the terms: 383 + -40x + x2 = 0 Solving 383 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-383' to each side of the equation. 383 + -40x + -383 + x2 = 0 + -383 Reorder the terms: 383 + -383 + -40x + x2 = 0 + -383 Combine like terms: 383 + -383 = 0 0 + -40x + x2 = 0 + -383 -40x + x2 = 0 + -383 Combine like terms: 0 + -383 = -383 -40x + x2 = -383 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 = -383 + 400 Reorder the terms: 400 + -40x + x2 = -383 + 400 Combine like terms: -383 + 400 = 17 400 + -40x + x2 = 17 Factor a perfect square on the left side: (x + -20)(x + -20) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -20) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -20 = 4.123105626 Simplifying x + -20 = 4.123105626 Reorder the terms: -20 + x = 4.123105626 Solving -20 + x = 4.123105626 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 = 4.123105626 + 20 Combine like terms: -20 + 20 = 0 0 + x = 4.123105626 + 20 x = 4.123105626 + 20 Combine like terms: 4.123105626 + 20 = 24.123105626 x = 24.123105626 Simplifying x = 24.123105626Subproblem 2
x + -20 = -4.123105626 Simplifying x + -20 = -4.123105626 Reorder the terms: -20 + x = -4.123105626 Solving -20 + x = -4.123105626 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 = -4.123105626 + 20 Combine like terms: -20 + 20 = 0 0 + x = -4.123105626 + 20 x = -4.123105626 + 20 Combine like terms: -4.123105626 + 20 = 15.876894374 x = 15.876894374 Simplifying x = 15.876894374Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.123105626, 15.876894374}
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