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Simplifying x2 + -26x + 10.2 = 0 Reorder the terms: 10.2 + -26x + x2 = 0 Solving 10.2 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10.2' to each side of the equation. 10.2 + -26x + -10.2 + x2 = 0 + -10.2 Reorder the terms: 10.2 + -10.2 + -26x + x2 = 0 + -10.2 Combine like terms: 10.2 + -10.2 = 0.0 0.0 + -26x + x2 = 0 + -10.2 -26x + x2 = 0 + -10.2 Combine like terms: 0 + -10.2 = -10.2 -26x + x2 = -10.2 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = -10.2 + 169 Reorder the terms: 169 + -26x + x2 = -10.2 + 169 Combine like terms: -10.2 + 169 = 158.8 169 + -26x + x2 = 158.8 Factor a perfect square on the left side: (x + -13)(x + -13) = 158.8 Calculate the square root of the right side: 12.601587202 Break this problem into two subproblems by setting (x + -13) equal to 12.601587202 and -12.601587202.Subproblem 1
x + -13 = 12.601587202 Simplifying x + -13 = 12.601587202 Reorder the terms: -13 + x = 12.601587202 Solving -13 + x = 12.601587202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 12.601587202 + 13 Combine like terms: -13 + 13 = 0 0 + x = 12.601587202 + 13 x = 12.601587202 + 13 Combine like terms: 12.601587202 + 13 = 25.601587202 x = 25.601587202 Simplifying x = 25.601587202Subproblem 2
x + -13 = -12.601587202 Simplifying x + -13 = -12.601587202 Reorder the terms: -13 + x = -12.601587202 Solving -13 + x = -12.601587202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -12.601587202 + 13 Combine like terms: -13 + 13 = 0 0 + x = -12.601587202 + 13 x = -12.601587202 + 13 Combine like terms: -12.601587202 + 13 = 0.398412798 x = 0.398412798 Simplifying x = 0.398412798Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.601587202, 0.398412798}
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