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Simplifying x2 + 40x + 53 = 0 Reorder the terms: 53 + 40x + x2 = 0 Solving 53 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 40x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 40x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 40x + x2 = 0 + -53 40x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 40x + x2 = -53 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 = -53 + 400 Reorder the terms: 400 + 40x + x2 = -53 + 400 Combine like terms: -53 + 400 = 347 400 + 40x + x2 = 347 Factor a perfect square on the left side: (x + 20)(x + 20) = 347 Calculate the square root of the right side: 18.62793601 Break this problem into two subproblems by setting (x + 20) equal to 18.62793601 and -18.62793601.Subproblem 1
x + 20 = 18.62793601 Simplifying x + 20 = 18.62793601 Reorder the terms: 20 + x = 18.62793601 Solving 20 + x = 18.62793601 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 = 18.62793601 + -20 Combine like terms: 20 + -20 = 0 0 + x = 18.62793601 + -20 x = 18.62793601 + -20 Combine like terms: 18.62793601 + -20 = -1.37206399 x = -1.37206399 Simplifying x = -1.37206399Subproblem 2
x + 20 = -18.62793601 Simplifying x + 20 = -18.62793601 Reorder the terms: 20 + x = -18.62793601 Solving 20 + x = -18.62793601 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 = -18.62793601 + -20 Combine like terms: 20 + -20 = 0 0 + x = -18.62793601 + -20 x = -18.62793601 + -20 Combine like terms: -18.62793601 + -20 = -38.62793601 x = -38.62793601 Simplifying x = -38.62793601Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.37206399, -38.62793601}
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