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Simplifying (x + 7) + (x + 5) + (x2 + -3) + (4x + -3) = 49 Reorder the terms: (7 + x) + (x + 5) + (x2 + -3) + (4x + -3) = 49 Remove parenthesis around (7 + x) 7 + x + (x + 5) + (x2 + -3) + (4x + -3) = 49 Reorder the terms: 7 + x + (5 + x) + (x2 + -3) + (4x + -3) = 49 Remove parenthesis around (5 + x) 7 + x + 5 + x + (x2 + -3) + (4x + -3) = 49 Reorder the terms: 7 + x + 5 + x + (-3 + x2) + (4x + -3) = 49 Remove parenthesis around (-3 + x2) 7 + x + 5 + x + -3 + x2 + (4x + -3) = 49 Reorder the terms: 7 + x + 5 + x + -3 + x2 + (-3 + 4x) = 49 Remove parenthesis around (-3 + 4x) 7 + x + 5 + x + -3 + x2 + -3 + 4x = 49 Reorder the terms: 7 + 5 + -3 + -3 + x + x + 4x + x2 = 49 Combine like terms: 7 + 5 = 12 12 + -3 + -3 + x + x + 4x + x2 = 49 Combine like terms: 12 + -3 = 9 9 + -3 + x + x + 4x + x2 = 49 Combine like terms: 9 + -3 = 6 6 + x + x + 4x + x2 = 49 Combine like terms: x + x = 2x 6 + 2x + 4x + x2 = 49 Combine like terms: 2x + 4x = 6x 6 + 6x + x2 = 49 Solving 6 + 6x + x2 = 49 Solving for variable 'x'. Reorder the terms: 6 + -49 + 6x + x2 = 49 + -49 Combine like terms: 6 + -49 = -43 -43 + 6x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -43 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + 6x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + 6x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 6x + x2 = 0 + 43 6x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 6x + x2 = 43 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 43 + 9 Reorder the terms: 9 + 6x + x2 = 43 + 9 Combine like terms: 43 + 9 = 52 9 + 6x + x2 = 52 Factor a perfect square on the left side: (x + 3)(x + 3) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + 3) equal to 7.211102551 and -7.211102551.Subproblem 1
x + 3 = 7.211102551 Simplifying x + 3 = 7.211102551 Reorder the terms: 3 + x = 7.211102551 Solving 3 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 7.211102551 + -3 Combine like terms: 3 + -3 = 0 0 + x = 7.211102551 + -3 x = 7.211102551 + -3 Combine like terms: 7.211102551 + -3 = 4.211102551 x = 4.211102551 Simplifying x = 4.211102551Subproblem 2
x + 3 = -7.211102551 Simplifying x + 3 = -7.211102551 Reorder the terms: 3 + x = -7.211102551 Solving 3 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -7.211102551 + -3 Combine like terms: 3 + -3 = 0 0 + x = -7.211102551 + -3 x = -7.211102551 + -3 Combine like terms: -7.211102551 + -3 = -10.211102551 x = -10.211102551 Simplifying x = -10.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.211102551, -10.211102551}
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