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Simplifying x2 + 4x + -960 = 0 Reorder the terms: -960 + 4x + x2 = 0 Solving -960 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '960' to each side of the equation. -960 + 4x + 960 + x2 = 0 + 960 Reorder the terms: -960 + 960 + 4x + x2 = 0 + 960 Combine like terms: -960 + 960 = 0 0 + 4x + x2 = 0 + 960 4x + x2 = 0 + 960 Combine like terms: 0 + 960 = 960 4x + x2 = 960 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 = 960 + 4 Reorder the terms: 4 + 4x + x2 = 960 + 4 Combine like terms: 960 + 4 = 964 4 + 4x + x2 = 964 Factor a perfect square on the left side: (x + 2)(x + 2) = 964 Calculate the square root of the right side: 31.048349393 Break this problem into two subproblems by setting (x + 2) equal to 31.048349393 and -31.048349393.Subproblem 1
x + 2 = 31.048349393 Simplifying x + 2 = 31.048349393 Reorder the terms: 2 + x = 31.048349393 Solving 2 + x = 31.048349393 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 = 31.048349393 + -2 Combine like terms: 2 + -2 = 0 0 + x = 31.048349393 + -2 x = 31.048349393 + -2 Combine like terms: 31.048349393 + -2 = 29.048349393 x = 29.048349393 Simplifying x = 29.048349393Subproblem 2
x + 2 = -31.048349393 Simplifying x + 2 = -31.048349393 Reorder the terms: 2 + x = -31.048349393 Solving 2 + x = -31.048349393 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 = -31.048349393 + -2 Combine like terms: 2 + -2 = 0 0 + x = -31.048349393 + -2 x = -31.048349393 + -2 Combine like terms: -31.048349393 + -2 = -33.048349393 x = -33.048349393 Simplifying x = -33.048349393Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.048349393, -33.048349393}
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