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Simplifying ((x2) + 4x + -3128) = 0 (x2 + 4x + -3128) = 0 Reorder the terms: (-3128 + 4x + x2) = 0 Remove parenthesis around (-3128 + 4x + x2) -3128 + 4x + x2 = 0 Solving -3128 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3128' to each side of the equation. -3128 + 4x + 3128 + x2 = 0 + 3128 Reorder the terms: -3128 + 3128 + 4x + x2 = 0 + 3128 Combine like terms: -3128 + 3128 = 0 0 + 4x + x2 = 0 + 3128 4x + x2 = 0 + 3128 Combine like terms: 0 + 3128 = 3128 4x + x2 = 3128 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3128 + 4 Reorder the terms: 4 + 4x + x2 = 3128 + 4 Combine like terms: 3128 + 4 = 3132 4 + 4x + x2 = 3132 Factor a perfect square on the left side: (x + 2)(x + 2) = 3132 Calculate the square root of the right side: 55.964274319 Break this problem into two subproblems by setting (x + 2) equal to 55.964274319 and -55.964274319.Subproblem 1
x + 2 = 55.964274319 Simplifying x + 2 = 55.964274319 Reorder the terms: 2 + x = 55.964274319 Solving 2 + x = 55.964274319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 55.964274319 + -2 Combine like terms: 2 + -2 = 0 0 + x = 55.964274319 + -2 x = 55.964274319 + -2 Combine like terms: 55.964274319 + -2 = 53.964274319 x = 53.964274319 Simplifying x = 53.964274319Subproblem 2
x + 2 = -55.964274319 Simplifying x + 2 = -55.964274319 Reorder the terms: 2 + x = -55.964274319 Solving 2 + x = -55.964274319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -55.964274319 + -2 Combine like terms: 2 + -2 = 0 0 + x = -55.964274319 + -2 x = -55.964274319 + -2 Combine like terms: -55.964274319 + -2 = -57.964274319 x = -57.964274319 Simplifying x = -57.964274319Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.964274319, -57.964274319}
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