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Simplifying 2X2 + 8X = X2 + -6X + 9 Reorder the terms: 8X + 2X2 = X2 + -6X + 9 Reorder the terms: 8X + 2X2 = 9 + -6X + X2 Solving 8X + 2X2 = 9 + -6X + X2 Solving for variable 'X'. Reorder the terms: -9 + 8X + 6X + 2X2 + -1X2 = 9 + -6X + X2 + -9 + 6X + -1X2 Combine like terms: 8X + 6X = 14X -9 + 14X + 2X2 + -1X2 = 9 + -6X + X2 + -9 + 6X + -1X2 Combine like terms: 2X2 + -1X2 = 1X2 -9 + 14X + 1X2 = 9 + -6X + X2 + -9 + 6X + -1X2 Reorder the terms: -9 + 14X + 1X2 = 9 + -9 + -6X + 6X + X2 + -1X2 Combine like terms: 9 + -9 = 0 -9 + 14X + 1X2 = 0 + -6X + 6X + X2 + -1X2 -9 + 14X + 1X2 = -6X + 6X + X2 + -1X2 Combine like terms: -6X + 6X = 0 -9 + 14X + 1X2 = 0 + X2 + -1X2 -9 + 14X + 1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 -9 + 14X + 1X2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 14X + 9 + X2 = 0 + 9 Reorder the terms: -9 + 9 + 14X + X2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 14X + X2 = 0 + 9 14X + X2 = 0 + 9 Combine like terms: 0 + 9 = 9 14X + X2 = 9 The X term is 14X. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14X + 49 + X2 = 9 + 49 Reorder the terms: 49 + 14X + X2 = 9 + 49 Combine like terms: 9 + 49 = 58 49 + 14X + X2 = 58 Factor a perfect square on the left side: (X + 7)(X + 7) = 58 Calculate the square root of the right side: 7.615773106 Break this problem into two subproblems by setting (X + 7) equal to 7.615773106 and -7.615773106.Subproblem 1
X + 7 = 7.615773106 Simplifying X + 7 = 7.615773106 Reorder the terms: 7 + X = 7.615773106 Solving 7 + X = 7.615773106 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = 7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + X = 7.615773106 + -7 X = 7.615773106 + -7 Combine like terms: 7.615773106 + -7 = 0.615773106 X = 0.615773106 Simplifying X = 0.615773106Subproblem 2
X + 7 = -7.615773106 Simplifying X + 7 = -7.615773106 Reorder the terms: 7 + X = -7.615773106 Solving 7 + X = -7.615773106 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + X = -7.615773106 + -7 Combine like terms: 7 + -7 = 0 0 + X = -7.615773106 + -7 X = -7.615773106 + -7 Combine like terms: -7.615773106 + -7 = -14.615773106 X = -14.615773106 Simplifying X = -14.615773106Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.615773106, -14.615773106}
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