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Simplifying x2 + 25x + 7 = 0 Reorder the terms: 7 + 25x + x2 = 0 Solving 7 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 25x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 25x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 25x + x2 = 0 + -7 25x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 25x + x2 = -7 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 = -7 + 156.25 Reorder the terms: 156.25 + 25x + x2 = -7 + 156.25 Combine like terms: -7 + 156.25 = 149.25 156.25 + 25x + x2 = 149.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 149.25 Calculate the square root of the right side: 12.216791723 Break this problem into two subproblems by setting (x + 12.5) equal to 12.216791723 and -12.216791723.Subproblem 1
x + 12.5 = 12.216791723 Simplifying x + 12.5 = 12.216791723 Reorder the terms: 12.5 + x = 12.216791723 Solving 12.5 + x = 12.216791723 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 = 12.216791723 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 12.216791723 + -12.5 x = 12.216791723 + -12.5 Combine like terms: 12.216791723 + -12.5 = -0.283208277 x = -0.283208277 Simplifying x = -0.283208277Subproblem 2
x + 12.5 = -12.216791723 Simplifying x + 12.5 = -12.216791723 Reorder the terms: 12.5 + x = -12.216791723 Solving 12.5 + x = -12.216791723 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 = -12.216791723 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -12.216791723 + -12.5 x = -12.216791723 + -12.5 Combine like terms: -12.216791723 + -12.5 = -24.716791723 x = -24.716791723 Simplifying x = -24.716791723Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.283208277, -24.716791723}
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