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Simplifying x2 + 25x + -73 = 0 Reorder the terms: -73 + 25x + x2 = 0 Solving -73 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + 25x + 73 + x2 = 0 + 73 Reorder the terms: -73 + 73 + 25x + x2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + 25x + x2 = 0 + 73 25x + x2 = 0 + 73 Combine like terms: 0 + 73 = 73 25x + x2 = 73 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 = 73 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 73 + 156.25 Combine like terms: 73 + 156.25 = 229.25 156.25 + 25x + x2 = 229.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 229.25 Calculate the square root of the right side: 15.14100393 Break this problem into two subproblems by setting (x + 12.5) equal to 15.14100393 and -15.14100393.Subproblem 1
x + 12.5 = 15.14100393 Simplifying x + 12.5 = 15.14100393 Reorder the terms: 12.5 + x = 15.14100393 Solving 12.5 + x = 15.14100393 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 = 15.14100393 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 15.14100393 + -12.5 x = 15.14100393 + -12.5 Combine like terms: 15.14100393 + -12.5 = 2.64100393 x = 2.64100393 Simplifying x = 2.64100393Subproblem 2
x + 12.5 = -15.14100393 Simplifying x + 12.5 = -15.14100393 Reorder the terms: 12.5 + x = -15.14100393 Solving 12.5 + x = -15.14100393 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 = -15.14100393 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -15.14100393 + -12.5 x = -15.14100393 + -12.5 Combine like terms: -15.14100393 + -12.5 = -27.64100393 x = -27.64100393 Simplifying x = -27.64100393Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.64100393, -27.64100393}
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