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Simplifying (x + -9) * x = 97 Reorder the terms: (-9 + x) * x = 97 Reorder the terms for easier multiplication: x(-9 + x) = 97 (-9 * x + x * x) = 97 (-9x + x2) = 97 Solving -9x + x2 = 97 Solving for variable 'x'. Reorder the terms: -97 + -9x + x2 = 97 + -97 Combine like terms: 97 + -97 = 0 -97 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '97' to each side of the equation. -97 + -9x + 97 + x2 = 0 + 97 Reorder the terms: -97 + 97 + -9x + x2 = 0 + 97 Combine like terms: -97 + 97 = 0 0 + -9x + x2 = 0 + 97 -9x + x2 = 0 + 97 Combine like terms: 0 + 97 = 97 -9x + x2 = 97 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 97 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 97 + 20.25 Combine like terms: 97 + 20.25 = 117.25 20.25 + -9x + x2 = 117.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 117.25 Calculate the square root of the right side: 10.828203914 Break this problem into two subproblems by setting (x + -4.5) equal to 10.828203914 and -10.828203914.Subproblem 1
x + -4.5 = 10.828203914 Simplifying x + -4.5 = 10.828203914 Reorder the terms: -4.5 + x = 10.828203914 Solving -4.5 + x = 10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 10.828203914 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 10.828203914 + 4.5 x = 10.828203914 + 4.5 Combine like terms: 10.828203914 + 4.5 = 15.328203914 x = 15.328203914 Simplifying x = 15.328203914Subproblem 2
x + -4.5 = -10.828203914 Simplifying x + -4.5 = -10.828203914 Reorder the terms: -4.5 + x = -10.828203914 Solving -4.5 + x = -10.828203914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -10.828203914 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -10.828203914 + 4.5 x = -10.828203914 + 4.5 Combine like terms: -10.828203914 + 4.5 = -6.328203914 x = -6.328203914 Simplifying x = -6.328203914Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.328203914, -6.328203914}
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