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Simplifying (x + 7)(x + -3) = 4225 Reorder the terms: (7 + x)(x + -3) = 4225 Reorder the terms: (7 + x)(-3 + x) = 4225 Multiply (7 + x) * (-3 + x) (7(-3 + x) + x(-3 + x)) = 4225 ((-3 * 7 + x * 7) + x(-3 + x)) = 4225 ((-21 + 7x) + x(-3 + x)) = 4225 (-21 + 7x + (-3 * x + x * x)) = 4225 (-21 + 7x + (-3x + x2)) = 4225 Combine like terms: 7x + -3x = 4x (-21 + 4x + x2) = 4225 Solving -21 + 4x + x2 = 4225 Solving for variable 'x'. Reorder the terms: -21 + -4225 + 4x + x2 = 4225 + -4225 Combine like terms: -21 + -4225 = -4246 -4246 + 4x + x2 = 4225 + -4225 Combine like terms: 4225 + -4225 = 0 -4246 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4246' to each side of the equation. -4246 + 4x + 4246 + x2 = 0 + 4246 Reorder the terms: -4246 + 4246 + 4x + x2 = 0 + 4246 Combine like terms: -4246 + 4246 = 0 0 + 4x + x2 = 0 + 4246 4x + x2 = 0 + 4246 Combine like terms: 0 + 4246 = 4246 4x + x2 = 4246 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 4246 + 4 Reorder the terms: 4 + 4x + x2 = 4246 + 4 Combine like terms: 4246 + 4 = 4250 4 + 4x + x2 = 4250 Factor a perfect square on the left side: (x + 2)(x + 2) = 4250 Calculate the square root of the right side: 65.192024052 Break this problem into two subproblems by setting (x + 2) equal to 65.192024052 and -65.192024052.Subproblem 1
x + 2 = 65.192024052 Simplifying x + 2 = 65.192024052 Reorder the terms: 2 + x = 65.192024052 Solving 2 + x = 65.192024052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 65.192024052 + -2 Combine like terms: 2 + -2 = 0 0 + x = 65.192024052 + -2 x = 65.192024052 + -2 Combine like terms: 65.192024052 + -2 = 63.192024052 x = 63.192024052 Simplifying x = 63.192024052Subproblem 2
x + 2 = -65.192024052 Simplifying x + 2 = -65.192024052 Reorder the terms: 2 + x = -65.192024052 Solving 2 + x = -65.192024052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -65.192024052 + -2 Combine like terms: 2 + -2 = 0 0 + x = -65.192024052 + -2 x = -65.192024052 + -2 Combine like terms: -65.192024052 + -2 = -67.192024052 x = -67.192024052 Simplifying x = -67.192024052Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.192024052, -67.192024052}
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