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Simplifying x2 + -3x + -162 = 0 Reorder the terms: -162 + -3x + x2 = 0 Solving -162 + -3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '162' to each side of the equation. -162 + -3x + 162 + x2 = 0 + 162 Reorder the terms: -162 + 162 + -3x + x2 = 0 + 162 Combine like terms: -162 + 162 = 0 0 + -3x + x2 = 0 + 162 -3x + x2 = 0 + 162 Combine like terms: 0 + 162 = 162 -3x + x2 = 162 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 162 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 162 + 2.25 Combine like terms: 162 + 2.25 = 164.25 2.25 + -3x + x2 = 164.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (x + -1.5) equal to 12.816005618 and -12.816005618.Subproblem 1
x + -1.5 = 12.816005618 Simplifying x + -1.5 = 12.816005618 Reorder the terms: -1.5 + x = 12.816005618 Solving -1.5 + x = 12.816005618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 12.816005618 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.816005618 + 1.5 x = 12.816005618 + 1.5 Combine like terms: 12.816005618 + 1.5 = 14.316005618 x = 14.316005618 Simplifying x = 14.316005618Subproblem 2
x + -1.5 = -12.816005618 Simplifying x + -1.5 = -12.816005618 Reorder the terms: -1.5 + x = -12.816005618 Solving -1.5 + x = -12.816005618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -12.816005618 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.816005618 + 1.5 x = -12.816005618 + 1.5 Combine like terms: -12.816005618 + 1.5 = -11.316005618 x = -11.316005618 Simplifying x = -11.316005618Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.316005618, -11.316005618}
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