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Simplifying X * X = 12X + 17 Multiply X * X X2 = 12X + 17 Reorder the terms: X2 = 17 + 12X Solving X2 = 17 + 12X Solving for variable 'X'. Reorder the terms: -17 + -12X + X2 = 17 + 12X + -17 + -12X Reorder the terms: -17 + -12X + X2 = 17 + -17 + 12X + -12X Combine like terms: 17 + -17 = 0 -17 + -12X + X2 = 0 + 12X + -12X -17 + -12X + X2 = 12X + -12X Combine like terms: 12X + -12X = 0 -17 + -12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -12X + 17 + X2 = 0 + 17 Reorder the terms: -17 + 17 + -12X + X2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -12X + X2 = 0 + 17 -12X + X2 = 0 + 17 Combine like terms: 0 + 17 = 17 -12X + X2 = 17 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = 17 + 36 Reorder the terms: 36 + -12X + X2 = 17 + 36 Combine like terms: 17 + 36 = 53 36 + -12X + X2 = 53 Factor a perfect square on the left side: (X + -6)(X + -6) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (X + -6) equal to 7.280109889 and -7.280109889.Subproblem 1
X + -6 = 7.280109889 Simplifying X + -6 = 7.280109889 Reorder the terms: -6 + X = 7.280109889 Solving -6 + X = 7.280109889 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + X = 7.280109889 + 6 X = 7.280109889 + 6 Combine like terms: 7.280109889 + 6 = 13.280109889 X = 13.280109889 Simplifying X = 13.280109889Subproblem 2
X + -6 = -7.280109889 Simplifying X + -6 = -7.280109889 Reorder the terms: -6 + X = -7.280109889 Solving -6 + X = -7.280109889 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + X = -7.280109889 + 6 X = -7.280109889 + 6 Combine like terms: -7.280109889 + 6 = -1.280109889 X = -1.280109889 Simplifying X = -1.280109889Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.280109889, -1.280109889}
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