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Simplifying x2 + 260x + -3120 = 0 Reorder the terms: -3120 + 260x + x2 = 0 Solving -3120 + 260x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3120' to each side of the equation. -3120 + 260x + 3120 + x2 = 0 + 3120 Reorder the terms: -3120 + 3120 + 260x + x2 = 0 + 3120 Combine like terms: -3120 + 3120 = 0 0 + 260x + x2 = 0 + 3120 260x + x2 = 0 + 3120 Combine like terms: 0 + 3120 = 3120 260x + x2 = 3120 The x term is 260x. Take half its coefficient (130). Square it (16900) and add it to both sides. Add '16900' to each side of the equation. 260x + 16900 + x2 = 3120 + 16900 Reorder the terms: 16900 + 260x + x2 = 3120 + 16900 Combine like terms: 3120 + 16900 = 20020 16900 + 260x + x2 = 20020 Factor a perfect square on the left side: (x + 130)(x + 130) = 20020 Calculate the square root of the right side: 141.492049247 Break this problem into two subproblems by setting (x + 130) equal to 141.492049247 and -141.492049247.Subproblem 1
x + 130 = 141.492049247 Simplifying x + 130 = 141.492049247 Reorder the terms: 130 + x = 141.492049247 Solving 130 + x = 141.492049247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-130' to each side of the equation. 130 + -130 + x = 141.492049247 + -130 Combine like terms: 130 + -130 = 0 0 + x = 141.492049247 + -130 x = 141.492049247 + -130 Combine like terms: 141.492049247 + -130 = 11.492049247 x = 11.492049247 Simplifying x = 11.492049247Subproblem 2
x + 130 = -141.492049247 Simplifying x + 130 = -141.492049247 Reorder the terms: 130 + x = -141.492049247 Solving 130 + x = -141.492049247 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-130' to each side of the equation. 130 + -130 + x = -141.492049247 + -130 Combine like terms: 130 + -130 = 0 0 + x = -141.492049247 + -130 x = -141.492049247 + -130 Combine like terms: -141.492049247 + -130 = -271.492049247 x = -271.492049247 Simplifying x = -271.492049247Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.492049247, -271.492049247}
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