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Simplifying x2 + 40x + -784 = 0 Reorder the terms: -784 + 40x + x2 = 0 Solving -784 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '784' to each side of the equation. -784 + 40x + 784 + x2 = 0 + 784 Reorder the terms: -784 + 784 + 40x + x2 = 0 + 784 Combine like terms: -784 + 784 = 0 0 + 40x + x2 = 0 + 784 40x + x2 = 0 + 784 Combine like terms: 0 + 784 = 784 40x + x2 = 784 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 = 784 + 400 Reorder the terms: 400 + 40x + x2 = 784 + 400 Combine like terms: 784 + 400 = 1184 400 + 40x + x2 = 1184 Factor a perfect square on the left side: (x + 20)(x + 20) = 1184 Calculate the square root of the right side: 34.409301068 Break this problem into two subproblems by setting (x + 20) equal to 34.409301068 and -34.409301068.Subproblem 1
x + 20 = 34.409301068 Simplifying x + 20 = 34.409301068 Reorder the terms: 20 + x = 34.409301068 Solving 20 + x = 34.409301068 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 = 34.409301068 + -20 Combine like terms: 20 + -20 = 0 0 + x = 34.409301068 + -20 x = 34.409301068 + -20 Combine like terms: 34.409301068 + -20 = 14.409301068 x = 14.409301068 Simplifying x = 14.409301068Subproblem 2
x + 20 = -34.409301068 Simplifying x + 20 = -34.409301068 Reorder the terms: 20 + x = -34.409301068 Solving 20 + x = -34.409301068 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 = -34.409301068 + -20 Combine like terms: 20 + -20 = 0 0 + x = -34.409301068 + -20 x = -34.409301068 + -20 Combine like terms: -34.409301068 + -20 = -54.409301068 x = -54.409301068 Simplifying x = -54.409301068Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.409301068, -54.409301068}
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