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Simplifying -57600 + 14x + x2 = 0 Solving -57600 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '57600' to each side of the equation. -57600 + 14x + 57600 + x2 = 0 + 57600 Reorder the terms: -57600 + 57600 + 14x + x2 = 0 + 57600 Combine like terms: -57600 + 57600 = 0 0 + 14x + x2 = 0 + 57600 14x + x2 = 0 + 57600 Combine like terms: 0 + 57600 = 57600 14x + x2 = 57600 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 57600 + 49 Reorder the terms: 49 + 14x + x2 = 57600 + 49 Combine like terms: 57600 + 49 = 57649 49 + 14x + x2 = 57649 Factor a perfect square on the left side: (x + 7)(x + 7) = 57649 Calculate the square root of the right side: 240.102061632 Break this problem into two subproblems by setting (x + 7) equal to 240.102061632 and -240.102061632.Subproblem 1
x + 7 = 240.102061632 Simplifying x + 7 = 240.102061632 Reorder the terms: 7 + x = 240.102061632 Solving 7 + x = 240.102061632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 240.102061632 + -7 Combine like terms: 7 + -7 = 0 0 + x = 240.102061632 + -7 x = 240.102061632 + -7 Combine like terms: 240.102061632 + -7 = 233.102061632 x = 233.102061632 Simplifying x = 233.102061632Subproblem 2
x + 7 = -240.102061632 Simplifying x + 7 = -240.102061632 Reorder the terms: 7 + x = -240.102061632 Solving 7 + x = -240.102061632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -240.102061632 + -7 Combine like terms: 7 + -7 = 0 0 + x = -240.102061632 + -7 x = -240.102061632 + -7 Combine like terms: -240.102061632 + -7 = -247.102061632 x = -247.102061632 Simplifying x = -247.102061632Solution
The solution to the problem is based on the solutions from the subproblems. x = {233.102061632, -247.102061632}
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