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Simplifying 0 = x2 + 3x + -162 Reorder the terms: 0 = -162 + 3x + x2 Solving 0 = -162 + 3x + x2 Solving for variable 'x'. Combine like terms: 0 + 162 = 162 162 + -3x + -1x2 = -162 + 3x + x2 + 162 + -3x + -1x2 Reorder the terms: 162 + -3x + -1x2 = -162 + 162 + 3x + -3x + x2 + -1x2 Combine like terms: -162 + 162 = 0 162 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2 162 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 162 + -3x + -1x2 = 0 + x2 + -1x2 162 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 162 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -162 + 3x + x2 = 0 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 = 11.316005618 x = 11.316005618 Simplifying x = 11.316005618Subproblem 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 = -14.316005618 x = -14.316005618 Simplifying x = -14.316005618Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.316005618, -14.316005618}
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