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Simplifying X2 + -2.6X = 10.2 Reorder the terms: -2.6X + X2 = 10.2 Solving -2.6X + X2 = 10.2 Solving for variable 'X'. Reorder the terms: -10.2 + -2.6X + X2 = 10.2 + -10.2 Combine like terms: 10.2 + -10.2 = 0.0 -10.2 + -2.6X + X2 = 0.0 Begin completing the square. Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -2.6X + 10.2 + X2 = 0.0 + 10.2 Reorder the terms: -10.2 + 10.2 + -2.6X + X2 = 0.0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -2.6X + X2 = 0.0 + 10.2 -2.6X + X2 = 0.0 + 10.2 Combine like terms: 0.0 + 10.2 = 10.2 -2.6X + X2 = 10.2 The X term is -2.6X. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6X + 1.69 + X2 = 10.2 + 1.69 Reorder the terms: 1.69 + -2.6X + X2 = 10.2 + 1.69 Combine like terms: 10.2 + 1.69 = 11.89 1.69 + -2.6X + X2 = 11.89 Factor a perfect square on the left side: (X + -1.3)(X + -1.3) = 11.89 Calculate the square root of the right side: 3.44818793 Break this problem into two subproblems by setting (X + -1.3) equal to 3.44818793 and -3.44818793.Subproblem 1
X + -1.3 = 3.44818793 Simplifying X + -1.3 = 3.44818793 Reorder the terms: -1.3 + X = 3.44818793 Solving -1.3 + X = 3.44818793 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + X = 3.44818793 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + X = 3.44818793 + 1.3 X = 3.44818793 + 1.3 Combine like terms: 3.44818793 + 1.3 = 4.74818793 X = 4.74818793 Simplifying X = 4.74818793Subproblem 2
X + -1.3 = -3.44818793 Simplifying X + -1.3 = -3.44818793 Reorder the terms: -1.3 + X = -3.44818793 Solving -1.3 + X = -3.44818793 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + X = -3.44818793 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + X = -3.44818793 + 1.3 X = -3.44818793 + 1.3 Combine like terms: -3.44818793 + 1.3 = -2.14818793 X = -2.14818793 Simplifying X = -2.14818793Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.74818793, -2.14818793}
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