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Simplifying x2 + 4x + -260 = 0 Reorder the terms: -260 + 4x + x2 = 0 Solving -260 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '260' to each side of the equation. -260 + 4x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 4x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 4x + x2 = 0 + 260 4x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 4x + x2 = 260 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 = 260 + 4 Reorder the terms: 4 + 4x + x2 = 260 + 4 Combine like terms: 260 + 4 = 264 4 + 4x + x2 = 264 Factor a perfect square on the left side: (x + 2)(x + 2) = 264 Calculate the square root of the right side: 16.248076809 Break this problem into two subproblems by setting (x + 2) equal to 16.248076809 and -16.248076809.Subproblem 1
x + 2 = 16.248076809 Simplifying x + 2 = 16.248076809 Reorder the terms: 2 + x = 16.248076809 Solving 2 + x = 16.248076809 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 = 16.248076809 + -2 Combine like terms: 2 + -2 = 0 0 + x = 16.248076809 + -2 x = 16.248076809 + -2 Combine like terms: 16.248076809 + -2 = 14.248076809 x = 14.248076809 Simplifying x = 14.248076809Subproblem 2
x + 2 = -16.248076809 Simplifying x + 2 = -16.248076809 Reorder the terms: 2 + x = -16.248076809 Solving 2 + x = -16.248076809 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 = -16.248076809 + -2 Combine like terms: 2 + -2 = 0 0 + x = -16.248076809 + -2 x = -16.248076809 + -2 Combine like terms: -16.248076809 + -2 = -18.248076809 x = -18.248076809 Simplifying x = -18.248076809Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.248076809, -18.248076809}
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