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Simplifying (x + -4)(x + -6) = 65582565 Reorder the terms: (-4 + x)(x + -6) = 65582565 Reorder the terms: (-4 + x)(-6 + x) = 65582565 Multiply (-4 + x) * (-6 + x) (-4(-6 + x) + x(-6 + x)) = 65582565 ((-6 * -4 + x * -4) + x(-6 + x)) = 65582565 ((24 + -4x) + x(-6 + x)) = 65582565 (24 + -4x + (-6 * x + x * x)) = 65582565 (24 + -4x + (-6x + x2)) = 65582565 Combine like terms: -4x + -6x = -10x (24 + -10x + x2) = 65582565 Solving 24 + -10x + x2 = 65582565 Solving for variable 'x'. Reorder the terms: 24 + -65582565 + -10x + x2 = 65582565 + -65582565 Combine like terms: 24 + -65582565 = -65582541 -65582541 + -10x + x2 = 65582565 + -65582565 Combine like terms: 65582565 + -65582565 = 0 -65582541 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '65582541' to each side of the equation. -65582541 + -10x + 65582541 + x2 = 0 + 65582541 Reorder the terms: -65582541 + 65582541 + -10x + x2 = 0 + 65582541 Combine like terms: -65582541 + 65582541 = 0 0 + -10x + x2 = 0 + 65582541 -10x + x2 = 0 + 65582541 Combine like terms: 0 + 65582541 = 65582541 -10x + x2 = 65582541 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 65582541 + 25 Reorder the terms: 25 + -10x + x2 = 65582541 + 25 Combine like terms: 65582541 + 25 = 65582566 25 + -10x + x2 = 65582566 Factor a perfect square on the left side: (x + -5)(x + -5) = 65582566 Calculate the square root of the right side: 8098.306366148 Break this problem into two subproblems by setting (x + -5) equal to 8098.306366148 and -8098.306366148.Subproblem 1
x + -5 = 8098.306366148 Simplifying x + -5 = 8098.306366148 Reorder the terms: -5 + x = 8098.306366148 Solving -5 + x = 8098.306366148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 8098.306366148 + 5 Combine like terms: -5 + 5 = 0 0 + x = 8098.306366148 + 5 x = 8098.306366148 + 5 Combine like terms: 8098.306366148 + 5 = 8103.306366148 x = 8103.306366148 Simplifying x = 8103.306366148Subproblem 2
x + -5 = -8098.306366148 Simplifying x + -5 = -8098.306366148 Reorder the terms: -5 + x = -8098.306366148 Solving -5 + x = -8098.306366148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -8098.306366148 + 5 Combine like terms: -5 + 5 = 0 0 + x = -8098.306366148 + 5 x = -8098.306366148 + 5 Combine like terms: -8098.306366148 + 5 = -8093.306366148 x = -8093.306366148 Simplifying x = -8093.306366148Solution
The solution to the problem is based on the solutions from the subproblems. x = {8103.306366148, -8093.306366148}
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