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Simplifying 9 + -24x = -11x + 45 + -1x2 Reorder the terms: 9 + -24x = 45 + -11x + -1x2 Solving 9 + -24x = 45 + -11x + -1x2 Solving for variable 'x'. Reorder the terms: 9 + -45 + -24x + 11x + x2 = 45 + -11x + -1x2 + -45 + 11x + x2 Combine like terms: 9 + -45 = -36 -36 + -24x + 11x + x2 = 45 + -11x + -1x2 + -45 + 11x + x2 Combine like terms: -24x + 11x = -13x -36 + -13x + x2 = 45 + -11x + -1x2 + -45 + 11x + x2 Reorder the terms: -36 + -13x + x2 = 45 + -45 + -11x + 11x + -1x2 + x2 Combine like terms: 45 + -45 = 0 -36 + -13x + x2 = 0 + -11x + 11x + -1x2 + x2 -36 + -13x + x2 = -11x + 11x + -1x2 + x2 Combine like terms: -11x + 11x = 0 -36 + -13x + x2 = 0 + -1x2 + x2 -36 + -13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -36 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -13x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -13x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13x + x2 = 0 + 36 -13x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -13x + x2 = 36 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 36 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13x + x2 = 78.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -6.5 = 8.845903006 Simplifying x + -6.5 = 8.845903006 Reorder the terms: -6.5 + x = 8.845903006 Solving -6.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.845903006 + 6.5 x = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 x = 15.345903006 Simplifying x = 15.345903006Subproblem 2
x + -6.5 = -8.845903006 Simplifying x + -6.5 = -8.845903006 Reorder the terms: -6.5 + x = -8.845903006 Solving -6.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.845903006 + 6.5 x = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 x = -2.345903006 Simplifying x = -2.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.345903006, -2.345903006}
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