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Simplifying 1764 = (x + 3)(x + -8) Reorder the terms: 1764 = (3 + x)(x + -8) Reorder the terms: 1764 = (3 + x)(-8 + x) Multiply (3 + x) * (-8 + x) 1764 = (3(-8 + x) + x(-8 + x)) 1764 = ((-8 * 3 + x * 3) + x(-8 + x)) 1764 = ((-24 + 3x) + x(-8 + x)) 1764 = (-24 + 3x + (-8 * x + x * x)) 1764 = (-24 + 3x + (-8x + x2)) Combine like terms: 3x + -8x = -5x 1764 = (-24 + -5x + x2) Solving 1764 = -24 + -5x + x2 Solving for variable 'x'. Combine like terms: 1764 + 24 = 1788 1788 + 5x + -1x2 = -24 + -5x + x2 + 24 + 5x + -1x2 Reorder the terms: 1788 + 5x + -1x2 = -24 + 24 + -5x + 5x + x2 + -1x2 Combine like terms: -24 + 24 = 0 1788 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 1788 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 1788 + 5x + -1x2 = 0 + x2 + -1x2 1788 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1788 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1788 + -5x + x2 = 0 Move the constant term to the right: Add '1788' to each side of the equation. -1788 + -5x + 1788 + x2 = 0 + 1788 Reorder the terms: -1788 + 1788 + -5x + x2 = 0 + 1788 Combine like terms: -1788 + 1788 = 0 0 + -5x + x2 = 0 + 1788 -5x + x2 = 0 + 1788 Combine like terms: 0 + 1788 = 1788 -5x + x2 = 1788 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 = 1788 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 1788 + 6.25 Combine like terms: 1788 + 6.25 = 1794.25 6.25 + -5x + x2 = 1794.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1794.25 Calculate the square root of the right side: 42.358588267 Break this problem into two subproblems by setting (x + -2.5) equal to 42.358588267 and -42.358588267.Subproblem 1
x + -2.5 = 42.358588267 Simplifying x + -2.5 = 42.358588267 Reorder the terms: -2.5 + x = 42.358588267 Solving -2.5 + x = 42.358588267 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 = 42.358588267 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 42.358588267 + 2.5 x = 42.358588267 + 2.5 Combine like terms: 42.358588267 + 2.5 = 44.858588267 x = 44.858588267 Simplifying x = 44.858588267Subproblem 2
x + -2.5 = -42.358588267 Simplifying x + -2.5 = -42.358588267 Reorder the terms: -2.5 + x = -42.358588267 Solving -2.5 + x = -42.358588267 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 = -42.358588267 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -42.358588267 + 2.5 x = -42.358588267 + 2.5 Combine like terms: -42.358588267 + 2.5 = -39.858588267 x = -39.858588267 Simplifying x = -39.858588267Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.858588267, -39.858588267}
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