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Simplifying x2 + 25x + -29 = 0 Reorder the terms: -29 + 25x + x2 = 0 Solving -29 + 25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 25x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 25x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 25x + x2 = 0 + 29 25x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 25x + x2 = 29 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 = 29 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 29 + 156.25 Combine like terms: 29 + 156.25 = 185.25 156.25 + 25x + x2 = 185.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 185.25 Calculate the square root of the right side: 13.610657589 Break this problem into two subproblems by setting (x + 12.5) equal to 13.610657589 and -13.610657589.Subproblem 1
x + 12.5 = 13.610657589 Simplifying x + 12.5 = 13.610657589 Reorder the terms: 12.5 + x = 13.610657589 Solving 12.5 + x = 13.610657589 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 = 13.610657589 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 13.610657589 + -12.5 x = 13.610657589 + -12.5 Combine like terms: 13.610657589 + -12.5 = 1.110657589 x = 1.110657589 Simplifying x = 1.110657589Subproblem 2
x + 12.5 = -13.610657589 Simplifying x + 12.5 = -13.610657589 Reorder the terms: 12.5 + x = -13.610657589 Solving 12.5 + x = -13.610657589 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 = -13.610657589 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -13.610657589 + -12.5 x = -13.610657589 + -12.5 Combine like terms: -13.610657589 + -12.5 = -26.110657589 x = -26.110657589 Simplifying x = -26.110657589Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.110657589, -26.110657589}
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