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Simplifying x2 + -9x + -5 = 8x + 1 Reorder the terms: -5 + -9x + x2 = 8x + 1 Reorder the terms: -5 + -9x + x2 = 1 + 8x Solving -5 + -9x + x2 = 1 + 8x Solving for variable 'x'. Reorder the terms: -5 + -1 + -9x + -8x + x2 = 1 + 8x + -1 + -8x Combine like terms: -5 + -1 = -6 -6 + -9x + -8x + x2 = 1 + 8x + -1 + -8x Combine like terms: -9x + -8x = -17x -6 + -17x + x2 = 1 + 8x + -1 + -8x Reorder the terms: -6 + -17x + x2 = 1 + -1 + 8x + -8x Combine like terms: 1 + -1 = 0 -6 + -17x + x2 = 0 + 8x + -8x -6 + -17x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -6 + -17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -17x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -17x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -17x + x2 = 0 + 6 -17x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -17x + x2 = 6 The x term is -17x. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x + 72.25 + x2 = 6 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 6 + 72.25 Combine like terms: 6 + 72.25 = 78.25 72.25 + -17x + x2 = 78.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -8.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -8.5 = 8.845903006 Simplifying x + -8.5 = 8.845903006 Reorder the terms: -8.5 + x = 8.845903006 Solving -8.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.845903006 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.845903006 + 8.5 x = 8.845903006 + 8.5 Combine like terms: 8.845903006 + 8.5 = 17.345903006 x = 17.345903006 Simplifying x = 17.345903006Subproblem 2
x + -8.5 = -8.845903006 Simplifying x + -8.5 = -8.845903006 Reorder the terms: -8.5 + x = -8.845903006 Solving -8.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.845903006 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.845903006 + 8.5 x = -8.845903006 + 8.5 Combine like terms: -8.845903006 + 8.5 = -0.345903006 x = -0.345903006 Simplifying x = -0.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.345903006, -0.345903006}
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