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Simplifying 2x2 + -14x + 24 = x2 + -3x + 9 Reorder the terms: 24 + -14x + 2x2 = x2 + -3x + 9 Reorder the terms: 24 + -14x + 2x2 = 9 + -3x + x2 Solving 24 + -14x + 2x2 = 9 + -3x + x2 Solving for variable 'x'. Reorder the terms: 24 + -9 + -14x + 3x + 2x2 + -1x2 = 9 + -3x + x2 + -9 + 3x + -1x2 Combine like terms: 24 + -9 = 15 15 + -14x + 3x + 2x2 + -1x2 = 9 + -3x + x2 + -9 + 3x + -1x2 Combine like terms: -14x + 3x = -11x 15 + -11x + 2x2 + -1x2 = 9 + -3x + x2 + -9 + 3x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 15 + -11x + 1x2 = 9 + -3x + x2 + -9 + 3x + -1x2 Reorder the terms: 15 + -11x + 1x2 = 9 + -9 + -3x + 3x + x2 + -1x2 Combine like terms: 9 + -9 = 0 15 + -11x + 1x2 = 0 + -3x + 3x + x2 + -1x2 15 + -11x + 1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 15 + -11x + 1x2 = 0 + x2 + -1x2 15 + -11x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -11x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -11x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -11x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -11x + x2 = 0 + -15 -11x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -11x + x2 = -15 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -15 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -15 + 30.25 Combine like terms: -15 + 30.25 = 15.25 30.25 + -11x + x2 = 15.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -5.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -5.5 = 3.905124838 Simplifying x + -5.5 = 3.905124838 Reorder the terms: -5.5 + x = 3.905124838 Solving -5.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.905124838 + 5.5 x = 3.905124838 + 5.5 Combine like terms: 3.905124838 + 5.5 = 9.405124838 x = 9.405124838 Simplifying x = 9.405124838Subproblem 2
x + -5.5 = -3.905124838 Simplifying x + -5.5 = -3.905124838 Reorder the terms: -5.5 + x = -3.905124838 Solving -5.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -3.905124838 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.905124838 + 5.5 x = -3.905124838 + 5.5 Combine like terms: -3.905124838 + 5.5 = 1.594875162 x = 1.594875162 Simplifying x = 1.594875162Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.405124838, 1.594875162}
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