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Simplifying x2 + -4x + -1230 = 0 Reorder the terms: -1230 + -4x + x2 = 0 Solving -1230 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1230' to each side of the equation. -1230 + -4x + 1230 + x2 = 0 + 1230 Reorder the terms: -1230 + 1230 + -4x + x2 = 0 + 1230 Combine like terms: -1230 + 1230 = 0 0 + -4x + x2 = 0 + 1230 -4x + x2 = 0 + 1230 Combine like terms: 0 + 1230 = 1230 -4x + x2 = 1230 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 = 1230 + 4 Reorder the terms: 4 + -4x + x2 = 1230 + 4 Combine like terms: 1230 + 4 = 1234 4 + -4x + x2 = 1234 Factor a perfect square on the left side: (x + -2)(x + -2) = 1234 Calculate the square root of the right side: 35.128336141 Break this problem into two subproblems by setting (x + -2) equal to 35.128336141 and -35.128336141.Subproblem 1
x + -2 = 35.128336141 Simplifying x + -2 = 35.128336141 Reorder the terms: -2 + x = 35.128336141 Solving -2 + x = 35.128336141 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 = 35.128336141 + 2 Combine like terms: -2 + 2 = 0 0 + x = 35.128336141 + 2 x = 35.128336141 + 2 Combine like terms: 35.128336141 + 2 = 37.128336141 x = 37.128336141 Simplifying x = 37.128336141Subproblem 2
x + -2 = -35.128336141 Simplifying x + -2 = -35.128336141 Reorder the terms: -2 + x = -35.128336141 Solving -2 + x = -35.128336141 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 = -35.128336141 + 2 Combine like terms: -2 + 2 = 0 0 + x = -35.128336141 + 2 x = -35.128336141 + 2 Combine like terms: -35.128336141 + 2 = -33.128336141 x = -33.128336141 Simplifying x = -33.128336141Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.128336141, -33.128336141}
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