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Simplifying x2 + -59x + 385 = 0 Reorder the terms: 385 + -59x + x2 = 0 Solving 385 + -59x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-385' to each side of the equation. 385 + -59x + -385 + x2 = 0 + -385 Reorder the terms: 385 + -385 + -59x + x2 = 0 + -385 Combine like terms: 385 + -385 = 0 0 + -59x + x2 = 0 + -385 -59x + x2 = 0 + -385 Combine like terms: 0 + -385 = -385 -59x + x2 = -385 The x term is -59x. Take half its coefficient (-29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. -59x + 870.25 + x2 = -385 + 870.25 Reorder the terms: 870.25 + -59x + x2 = -385 + 870.25 Combine like terms: -385 + 870.25 = 485.25 870.25 + -59x + x2 = 485.25 Factor a perfect square on the left side: (x + -29.5)(x + -29.5) = 485.25 Calculate the square root of the right side: 22.028390772 Break this problem into two subproblems by setting (x + -29.5) equal to 22.028390772 and -22.028390772.Subproblem 1
x + -29.5 = 22.028390772 Simplifying x + -29.5 = 22.028390772 Reorder the terms: -29.5 + x = 22.028390772 Solving -29.5 + x = 22.028390772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = 22.028390772 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = 22.028390772 + 29.5 x = 22.028390772 + 29.5 Combine like terms: 22.028390772 + 29.5 = 51.528390772 x = 51.528390772 Simplifying x = 51.528390772Subproblem 2
x + -29.5 = -22.028390772 Simplifying x + -29.5 = -22.028390772 Reorder the terms: -29.5 + x = -22.028390772 Solving -29.5 + x = -22.028390772 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x = -22.028390772 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x = -22.028390772 + 29.5 x = -22.028390772 + 29.5 Combine like terms: -22.028390772 + 29.5 = 7.471609228 x = 7.471609228 Simplifying x = 7.471609228Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.528390772, 7.471609228}
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