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Simplifying x * x + 1x + 2x + 3x + 4 = 720 Multiply x * x x2 + 1x + 2x + 3x + 4 = 720 Reorder the terms: 4 + 1x + 2x + 3x + x2 = 720 Combine like terms: 1x + 2x = 3x 4 + 3x + 3x + x2 = 720 Combine like terms: 3x + 3x = 6x 4 + 6x + x2 = 720 Solving 4 + 6x + x2 = 720 Solving for variable 'x'. Reorder the terms: 4 + -720 + 6x + x2 = 720 + -720 Combine like terms: 4 + -720 = -716 -716 + 6x + x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -716 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '716' to each side of the equation. -716 + 6x + 716 + x2 = 0 + 716 Reorder the terms: -716 + 716 + 6x + x2 = 0 + 716 Combine like terms: -716 + 716 = 0 0 + 6x + x2 = 0 + 716 6x + x2 = 0 + 716 Combine like terms: 0 + 716 = 716 6x + x2 = 716 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 = 716 + 9 Reorder the terms: 9 + 6x + x2 = 716 + 9 Combine like terms: 716 + 9 = 725 9 + 6x + x2 = 725 Factor a perfect square on the left side: (x + 3)(x + 3) = 725 Calculate the square root of the right side: 26.925824036 Break this problem into two subproblems by setting (x + 3) equal to 26.925824036 and -26.925824036.Subproblem 1
x + 3 = 26.925824036 Simplifying x + 3 = 26.925824036 Reorder the terms: 3 + x = 26.925824036 Solving 3 + x = 26.925824036 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 = 26.925824036 + -3 Combine like terms: 3 + -3 = 0 0 + x = 26.925824036 + -3 x = 26.925824036 + -3 Combine like terms: 26.925824036 + -3 = 23.925824036 x = 23.925824036 Simplifying x = 23.925824036Subproblem 2
x + 3 = -26.925824036 Simplifying x + 3 = -26.925824036 Reorder the terms: 3 + x = -26.925824036 Solving 3 + x = -26.925824036 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 = -26.925824036 + -3 Combine like terms: 3 + -3 = 0 0 + x = -26.925824036 + -3 x = -26.925824036 + -3 Combine like terms: -26.925824036 + -3 = -29.925824036 x = -29.925824036 Simplifying x = -29.925824036Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.925824036, -29.925824036}
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