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Simplifying (x + 9)(x + -2) = 7 Reorder the terms: (9 + x)(x + -2) = 7 Reorder the terms: (9 + x)(-2 + x) = 7 Multiply (9 + x) * (-2 + x) (9(-2 + x) + x(-2 + x)) = 7 ((-2 * 9 + x * 9) + x(-2 + x)) = 7 ((-18 + 9x) + x(-2 + x)) = 7 (-18 + 9x + (-2 * x + x * x)) = 7 (-18 + 9x + (-2x + x2)) = 7 Combine like terms: 9x + -2x = 7x (-18 + 7x + x2) = 7 Solving -18 + 7x + x2 = 7 Solving for variable 'x'. Reorder the terms: -18 + -7 + 7x + x2 = 7 + -7 Combine like terms: -18 + -7 = -25 -25 + 7x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -25 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 7x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 7x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 7x + x2 = 0 + 25 7x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 7x + x2 = 25 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 25 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 25 + 12.25 Combine like terms: 25 + 12.25 = 37.25 12.25 + 7x + x2 = 37.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 37.25 Calculate the square root of the right side: 6.103277808 Break this problem into two subproblems by setting (x + 3.5) equal to 6.103277808 and -6.103277808.Subproblem 1
x + 3.5 = 6.103277808 Simplifying x + 3.5 = 6.103277808 Reorder the terms: 3.5 + x = 6.103277808 Solving 3.5 + x = 6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.103277808 + -3.5 x = 6.103277808 + -3.5 Combine like terms: 6.103277808 + -3.5 = 2.603277808 x = 2.603277808 Simplifying x = 2.603277808Subproblem 2
x + 3.5 = -6.103277808 Simplifying x + 3.5 = -6.103277808 Reorder the terms: 3.5 + x = -6.103277808 Solving 3.5 + x = -6.103277808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.103277808 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.103277808 + -3.5 x = -6.103277808 + -3.5 Combine like terms: -6.103277808 + -3.5 = -9.603277808 x = -9.603277808 Simplifying x = -9.603277808Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.603277808, -9.603277808}
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