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Simplifying (x + -1)(x + 3) = 15876 Reorder the terms: (-1 + x)(x + 3) = 15876 Reorder the terms: (-1 + x)(3 + x) = 15876 Multiply (-1 + x) * (3 + x) (-1(3 + x) + x(3 + x)) = 15876 ((3 * -1 + x * -1) + x(3 + x)) = 15876 ((-3 + -1x) + x(3 + x)) = 15876 (-3 + -1x + (3 * x + x * x)) = 15876 (-3 + -1x + (3x + x2)) = 15876 Combine like terms: -1x + 3x = 2x (-3 + 2x + x2) = 15876 Solving -3 + 2x + x2 = 15876 Solving for variable 'x'. Reorder the terms: -3 + -15876 + 2x + x2 = 15876 + -15876 Combine like terms: -3 + -15876 = -15879 -15879 + 2x + x2 = 15876 + -15876 Combine like terms: 15876 + -15876 = 0 -15879 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15879' to each side of the equation. -15879 + 2x + 15879 + x2 = 0 + 15879 Reorder the terms: -15879 + 15879 + 2x + x2 = 0 + 15879 Combine like terms: -15879 + 15879 = 0 0 + 2x + x2 = 0 + 15879 2x + x2 = 0 + 15879 Combine like terms: 0 + 15879 = 15879 2x + x2 = 15879 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 15879 + 1 Reorder the terms: 1 + 2x + x2 = 15879 + 1 Combine like terms: 15879 + 1 = 15880 1 + 2x + x2 = 15880 Factor a perfect square on the left side: (x + 1)(x + 1) = 15880 Calculate the square root of the right side: 126.015872016 Break this problem into two subproblems by setting (x + 1) equal to 126.015872016 and -126.015872016.Subproblem 1
x + 1 = 126.015872016 Simplifying x + 1 = 126.015872016 Reorder the terms: 1 + x = 126.015872016 Solving 1 + x = 126.015872016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 126.015872016 + -1 Combine like terms: 1 + -1 = 0 0 + x = 126.015872016 + -1 x = 126.015872016 + -1 Combine like terms: 126.015872016 + -1 = 125.015872016 x = 125.015872016 Simplifying x = 125.015872016Subproblem 2
x + 1 = -126.015872016 Simplifying x + 1 = -126.015872016 Reorder the terms: 1 + x = -126.015872016 Solving 1 + x = -126.015872016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -126.015872016 + -1 Combine like terms: 1 + -1 = 0 0 + x = -126.015872016 + -1 x = -126.015872016 + -1 Combine like terms: -126.015872016 + -1 = -127.015872016 x = -127.015872016 Simplifying x = -127.015872016Solution
The solution to the problem is based on the solutions from the subproblems. x = {125.015872016, -127.015872016}
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