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Simplifying (x + 7)(x + -9) = 25 Reorder the terms: (7 + x)(x + -9) = 25 Reorder the terms: (7 + x)(-9 + x) = 25 Multiply (7 + x) * (-9 + x) (7(-9 + x) + x(-9 + x)) = 25 ((-9 * 7 + x * 7) + x(-9 + x)) = 25 ((-63 + 7x) + x(-9 + x)) = 25 (-63 + 7x + (-9 * x + x * x)) = 25 (-63 + 7x + (-9x + x2)) = 25 Combine like terms: 7x + -9x = -2x (-63 + -2x + x2) = 25 Solving -63 + -2x + x2 = 25 Solving for variable 'x'. Reorder the terms: -63 + -25 + -2x + x2 = 25 + -25 Combine like terms: -63 + -25 = -88 -88 + -2x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -88 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -2x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -2x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -2x + x2 = 0 + 88 -2x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -2x + x2 = 88 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 = 88 + 1 Reorder the terms: 1 + -2x + x2 = 88 + 1 Combine like terms: 88 + 1 = 89 1 + -2x + x2 = 89 Factor a perfect square on the left side: (x + -1)(x + -1) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -1) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -1 = 9.433981132 Simplifying x + -1 = 9.433981132 Reorder the terms: -1 + x = 9.433981132 Solving -1 + x = 9.433981132 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 = 9.433981132 + 1 Combine like terms: -1 + 1 = 0 0 + x = 9.433981132 + 1 x = 9.433981132 + 1 Combine like terms: 9.433981132 + 1 = 10.433981132 x = 10.433981132 Simplifying x = 10.433981132Subproblem 2
x + -1 = -9.433981132 Simplifying x + -1 = -9.433981132 Reorder the terms: -1 + x = -9.433981132 Solving -1 + x = -9.433981132 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 = -9.433981132 + 1 Combine like terms: -1 + 1 = 0 0 + x = -9.433981132 + 1 x = -9.433981132 + 1 Combine like terms: -9.433981132 + 1 = -8.433981132 x = -8.433981132 Simplifying x = -8.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.433981132, -8.433981132}
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