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Simplifying x2 + 25x + 130 = 0 Reorder the terms: 130 + 25x + x2 = 0 Solving 130 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. 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 = -7.376524617 x = -7.376524617 Simplifying x = -7.376524617Subproblem 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 = -17.623475383 x = -17.623475383 Simplifying x = -17.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.376524617, -17.623475383}
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