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Simplifying x2 + 59x + 400 = 0 Reorder the terms: 400 + 59x + x2 = 0 Solving 400 + 59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-400' to each side of the equation. 400 + 59x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + 59x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + 59x + x2 = 0 + -400 59x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 59x + x2 = -400 The x term is 59x. Take half its coefficient (29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. 59x + 870.25 + x2 = -400 + 870.25 Reorder the terms: 870.25 + 59x + x2 = -400 + 870.25 Combine like terms: -400 + 870.25 = 470.25 870.25 + 59x + x2 = 470.25 Factor a perfect square on the left side: (x + 29.5)(x + 29.5) = 470.25 Calculate the square root of the right side: 21.685248442 Break this problem into two subproblems by setting (x + 29.5) equal to 21.685248442 and -21.685248442.Subproblem 1
x + 29.5 = 21.685248442 Simplifying x + 29.5 = 21.685248442 Reorder the terms: 29.5 + x = 21.685248442 Solving 29.5 + x = 21.685248442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = 21.685248442 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = 21.685248442 + -29.5 x = 21.685248442 + -29.5 Combine like terms: 21.685248442 + -29.5 = -7.814751558 x = -7.814751558 Simplifying x = -7.814751558Subproblem 2
x + 29.5 = -21.685248442 Simplifying x + 29.5 = -21.685248442 Reorder the terms: 29.5 + x = -21.685248442 Solving 29.5 + x = -21.685248442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-29.5' to each side of the equation. 29.5 + -29.5 + x = -21.685248442 + -29.5 Combine like terms: 29.5 + -29.5 = 0.0 0.0 + x = -21.685248442 + -29.5 x = -21.685248442 + -29.5 Combine like terms: -21.685248442 + -29.5 = -51.185248442 x = -51.185248442 Simplifying x = -51.185248442Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.814751558, -51.185248442}
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