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Simplifying x2 + 156x + 3559 = 0 Reorder the terms: 3559 + 156x + x2 = 0 Solving 3559 + 156x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3559' to each side of the equation. 3559 + 156x + -3559 + x2 = 0 + -3559 Reorder the terms: 3559 + -3559 + 156x + x2 = 0 + -3559 Combine like terms: 3559 + -3559 = 0 0 + 156x + x2 = 0 + -3559 156x + x2 = 0 + -3559 Combine like terms: 0 + -3559 = -3559 156x + x2 = -3559 The x term is 156x. Take half its coefficient (78). Square it (6084) and add it to both sides. Add '6084' to each side of the equation. 156x + 6084 + x2 = -3559 + 6084 Reorder the terms: 6084 + 156x + x2 = -3559 + 6084 Combine like terms: -3559 + 6084 = 2525 6084 + 156x + x2 = 2525 Factor a perfect square on the left side: (x + 78)(x + 78) = 2525 Calculate the square root of the right side: 50.249378106 Break this problem into two subproblems by setting (x + 78) equal to 50.249378106 and -50.249378106.Subproblem 1
x + 78 = 50.249378106 Simplifying x + 78 = 50.249378106 Reorder the terms: 78 + x = 50.249378106 Solving 78 + x = 50.249378106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = 50.249378106 + -78 Combine like terms: 78 + -78 = 0 0 + x = 50.249378106 + -78 x = 50.249378106 + -78 Combine like terms: 50.249378106 + -78 = -27.750621894 x = -27.750621894 Simplifying x = -27.750621894Subproblem 2
x + 78 = -50.249378106 Simplifying x + 78 = -50.249378106 Reorder the terms: 78 + x = -50.249378106 Solving 78 + x = -50.249378106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-78' to each side of the equation. 78 + -78 + x = -50.249378106 + -78 Combine like terms: 78 + -78 = 0 0 + x = -50.249378106 + -78 x = -50.249378106 + -78 Combine like terms: -50.249378106 + -78 = -128.249378106 x = -128.249378106 Simplifying x = -128.249378106Solution
The solution to the problem is based on the solutions from the subproblems. x = {-27.750621894, -128.249378106}
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