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Simplifying (x + 1)(x + 375) = 750 Reorder the terms: (1 + x)(x + 375) = 750 Reorder the terms: (1 + x)(375 + x) = 750 Multiply (1 + x) * (375 + x) (1(375 + x) + x(375 + x)) = 750 ((375 * 1 + x * 1) + x(375 + x)) = 750 ((375 + 1x) + x(375 + x)) = 750 (375 + 1x + (375 * x + x * x)) = 750 (375 + 1x + (375x + x2)) = 750 Combine like terms: 1x + 375x = 376x (375 + 376x + x2) = 750 Solving 375 + 376x + x2 = 750 Solving for variable 'x'. Reorder the terms: 375 + -750 + 376x + x2 = 750 + -750 Combine like terms: 375 + -750 = -375 -375 + 376x + x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -375 + 376x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '375' to each side of the equation. -375 + 376x + 375 + x2 = 0 + 375 Reorder the terms: -375 + 375 + 376x + x2 = 0 + 375 Combine like terms: -375 + 375 = 0 0 + 376x + x2 = 0 + 375 376x + x2 = 0 + 375 Combine like terms: 0 + 375 = 375 376x + x2 = 375 The x term is 376x. Take half its coefficient (188). Square it (35344) and add it to both sides. Add '35344' to each side of the equation. 376x + 35344 + x2 = 375 + 35344 Reorder the terms: 35344 + 376x + x2 = 375 + 35344 Combine like terms: 375 + 35344 = 35719 35344 + 376x + x2 = 35719 Factor a perfect square on the left side: (x + 188)(x + 188) = 35719 Calculate the square root of the right side: 188.994708921 Break this problem into two subproblems by setting (x + 188) equal to 188.994708921 and -188.994708921.Subproblem 1
x + 188 = 188.994708921 Simplifying x + 188 = 188.994708921 Reorder the terms: 188 + x = 188.994708921 Solving 188 + x = 188.994708921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-188' to each side of the equation. 188 + -188 + x = 188.994708921 + -188 Combine like terms: 188 + -188 = 0 0 + x = 188.994708921 + -188 x = 188.994708921 + -188 Combine like terms: 188.994708921 + -188 = 0.994708921 x = 0.994708921 Simplifying x = 0.994708921Subproblem 2
x + 188 = -188.994708921 Simplifying x + 188 = -188.994708921 Reorder the terms: 188 + x = -188.994708921 Solving 188 + x = -188.994708921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-188' to each side of the equation. 188 + -188 + x = -188.994708921 + -188 Combine like terms: 188 + -188 = 0 0 + x = -188.994708921 + -188 x = -188.994708921 + -188 Combine like terms: -188.994708921 + -188 = -376.994708921 x = -376.994708921 Simplifying x = -376.994708921Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.994708921, -376.994708921}
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