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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 = 22.484995497 x = 22.484995497 Simplifying x = 22.484995497Subproblem 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 = -27.484995497 x = -27.484995497 Simplifying x = -27.484995497Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.484995497, -27.484995497}
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