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Simplifying (x + -2)(x + -3) = 624 Reorder the terms: (-2 + x)(x + -3) = 624 Reorder the terms: (-2 + x)(-3 + x) = 624 Multiply (-2 + x) * (-3 + x) (-2(-3 + x) + x(-3 + x)) = 624 ((-3 * -2 + x * -2) + x(-3 + x)) = 624 ((6 + -2x) + x(-3 + x)) = 624 (6 + -2x + (-3 * x + x * x)) = 624 (6 + -2x + (-3x + x2)) = 624 Combine like terms: -2x + -3x = -5x (6 + -5x + x2) = 624 Solving 6 + -5x + x2 = 624 Solving for variable 'x'. Reorder the terms: 6 + -624 + -5x + x2 = 624 + -624 Combine like terms: 6 + -624 = -618 -618 + -5x + x2 = 624 + -624 Combine like terms: 624 + -624 = 0 -618 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '618' to each side of the equation. -618 + -5x + 618 + x2 = 0 + 618 Reorder the terms: -618 + 618 + -5x + x2 = 0 + 618 Combine like terms: -618 + 618 = 0 0 + -5x + x2 = 0 + 618 -5x + x2 = 0 + 618 Combine like terms: 0 + 618 = 618 -5x + x2 = 618 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 618 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 618 + 6.25 Combine like terms: 618 + 6.25 = 624.25 6.25 + -5x + x2 = 624.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 624.25 Calculate the square root of the right side: 24.984995497 Break this problem into two subproblems by setting (x + -2.5) equal to 24.984995497 and -24.984995497.Subproblem 1
x + -2.5 = 24.984995497 Simplifying x + -2.5 = 24.984995497 Reorder the terms: -2.5 + x = 24.984995497 Solving -2.5 + x = 24.984995497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 24.984995497 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 24.984995497 + 2.5 x = 24.984995497 + 2.5 Combine like terms: 24.984995497 + 2.5 = 27.484995497 x = 27.484995497 Simplifying x = 27.484995497Subproblem 2
x + -2.5 = -24.984995497 Simplifying x + -2.5 = -24.984995497 Reorder the terms: -2.5 + x = -24.984995497 Solving -2.5 + x = -24.984995497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -24.984995497 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -24.984995497 + 2.5 x = -24.984995497 + 2.5 Combine like terms: -24.984995497 + 2.5 = -22.484995497 x = -22.484995497 Simplifying x = -22.484995497Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.484995497, -22.484995497}
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