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Simplifying x2 + -4x + -232 = 0 Reorder the terms: -232 + -4x + x2 = 0 Solving -232 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '232' to each side of the equation. -232 + -4x + 232 + x2 = 0 + 232 Reorder the terms: -232 + 232 + -4x + x2 = 0 + 232 Combine like terms: -232 + 232 = 0 0 + -4x + x2 = 0 + 232 -4x + x2 = 0 + 232 Combine like terms: 0 + 232 = 232 -4x + x2 = 232 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 = 232 + 4 Reorder the terms: 4 + -4x + x2 = 232 + 4 Combine like terms: 232 + 4 = 236 4 + -4x + x2 = 236 Factor a perfect square on the left side: (x + -2)(x + -2) = 236 Calculate the square root of the right side: 15.362291496 Break this problem into two subproblems by setting (x + -2) equal to 15.362291496 and -15.362291496.Subproblem 1
x + -2 = 15.362291496 Simplifying x + -2 = 15.362291496 Reorder the terms: -2 + x = 15.362291496 Solving -2 + x = 15.362291496 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 = 15.362291496 + 2 Combine like terms: -2 + 2 = 0 0 + x = 15.362291496 + 2 x = 15.362291496 + 2 Combine like terms: 15.362291496 + 2 = 17.362291496 x = 17.362291496 Simplifying x = 17.362291496Subproblem 2
x + -2 = -15.362291496 Simplifying x + -2 = -15.362291496 Reorder the terms: -2 + x = -15.362291496 Solving -2 + x = -15.362291496 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 = -15.362291496 + 2 Combine like terms: -2 + 2 = 0 0 + x = -15.362291496 + 2 x = -15.362291496 + 2 Combine like terms: -15.362291496 + 2 = -13.362291496 x = -13.362291496 Simplifying x = -13.362291496Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.362291496, -13.362291496}
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