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Simplifying x2 + 4x + 4(10) = 40(x + 2) Multiply 4 * 10 x2 + 4x + 40 = 40(x + 2) Reorder the terms: 40 + 4x + x2 = 40(x + 2) Reorder the terms: 40 + 4x + x2 = 40(2 + x) 40 + 4x + x2 = (2 * 40 + x * 40) 40 + 4x + x2 = (80 + 40x) Solving 40 + 4x + x2 = 80 + 40x Solving for variable 'x'. Reorder the terms: 40 + -80 + 4x + -40x + x2 = 80 + 40x + -80 + -40x Combine like terms: 40 + -80 = -40 -40 + 4x + -40x + x2 = 80 + 40x + -80 + -40x Combine like terms: 4x + -40x = -36x -40 + -36x + x2 = 80 + 40x + -80 + -40x Reorder the terms: -40 + -36x + x2 = 80 + -80 + 40x + -40x Combine like terms: 80 + -80 = 0 -40 + -36x + x2 = 0 + 40x + -40x -40 + -36x + x2 = 40x + -40x Combine like terms: 40x + -40x = 0 -40 + -36x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -36x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -36x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -36x + x2 = 0 + 40 -36x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -36x + x2 = 40 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = 40 + 324 Reorder the terms: 324 + -36x + x2 = 40 + 324 Combine like terms: 40 + 324 = 364 324 + -36x + x2 = 364 Factor a perfect square on the left side: (x + -18)(x + -18) = 364 Calculate the square root of the right side: 19.078784028 Break this problem into two subproblems by setting (x + -18) equal to 19.078784028 and -19.078784028.Subproblem 1
x + -18 = 19.078784028 Simplifying x + -18 = 19.078784028 Reorder the terms: -18 + x = 19.078784028 Solving -18 + x = 19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 19.078784028 + 18 Combine like terms: -18 + 18 = 0 0 + x = 19.078784028 + 18 x = 19.078784028 + 18 Combine like terms: 19.078784028 + 18 = 37.078784028 x = 37.078784028 Simplifying x = 37.078784028Subproblem 2
x + -18 = -19.078784028 Simplifying x + -18 = -19.078784028 Reorder the terms: -18 + x = -19.078784028 Solving -18 + x = -19.078784028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -19.078784028 + 18 Combine like terms: -18 + 18 = 0 0 + x = -19.078784028 + 18 x = -19.078784028 + 18 Combine like terms: -19.078784028 + 18 = -1.078784028 x = -1.078784028 Simplifying x = -1.078784028Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.078784028, -1.078784028}
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