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Simplifying 0 = x2 + -25x + 130 Reorder the terms: 0 = 130 + -25x + x2 Solving 0 = 130 + -25x + x2 Solving for variable 'x'. Combine like terms: 0 + -130 = -130 -130 + 25x + -1x2 = 130 + -25x + x2 + -130 + 25x + -1x2 Reorder the terms: -130 + 25x + -1x2 = 130 + -130 + -25x + 25x + x2 + -1x2 Combine like terms: 130 + -130 = 0 -130 + 25x + -1x2 = 0 + -25x + 25x + x2 + -1x2 -130 + 25x + -1x2 = -25x + 25x + x2 + -1x2 Combine like terms: -25x + 25x = 0 -130 + 25x + -1x2 = 0 + x2 + -1x2 -130 + 25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -130 + 25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 130 + -25x + x2 = 0 Move the constant term to the right: Add '-130' to each side of the equation. 130 + -25x + -130 + x2 = 0 + -130 Reorder the terms: 130 + -130 + -25x + x2 = 0 + -130 Combine like terms: 130 + -130 = 0 0 + -25x + x2 = 0 + -130 -25x + x2 = 0 + -130 Combine like terms: 0 + -130 = -130 -25x + x2 = -130 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -130 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -130 + 156.25 Combine like terms: -130 + 156.25 = 26.25 156.25 + -25x + x2 = 26.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -12.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -12.5 = 5.123475383 Simplifying x + -12.5 = 5.123475383 Reorder the terms: -12.5 + x = 5.123475383 Solving -12.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 5.123475383 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 5.123475383 + 12.5 x = 5.123475383 + 12.5 Combine like terms: 5.123475383 + 12.5 = 17.623475383 x = 17.623475383 Simplifying x = 17.623475383Subproblem 2
x + -12.5 = -5.123475383 Simplifying x + -12.5 = -5.123475383 Reorder the terms: -12.5 + x = -5.123475383 Solving -12.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -5.123475383 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -5.123475383 + 12.5 x = -5.123475383 + 12.5 Combine like terms: -5.123475383 + 12.5 = 7.376524617 x = 7.376524617 Simplifying x = 7.376524617Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.623475383, 7.376524617}
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