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Simplifying 25x2 + 50x + -8500 = 0 Reorder the terms: -8500 + 50x + 25x2 = 0 Solving -8500 + 50x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(-340 + 2x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-340 + 2x + x2)' equal to zero and attempt to solve: Simplifying -340 + 2x + x2 = 0 Solving -340 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '340' to each side of the equation. -340 + 2x + 340 + x2 = 0 + 340 Reorder the terms: -340 + 340 + 2x + x2 = 0 + 340 Combine like terms: -340 + 340 = 0 0 + 2x + x2 = 0 + 340 2x + x2 = 0 + 340 Combine like terms: 0 + 340 = 340 2x + x2 = 340 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 340 + 1 Reorder the terms: 1 + 2x + x2 = 340 + 1 Combine like terms: 340 + 1 = 341 1 + 2x + x2 = 341 Factor a perfect square on the left side: (x + 1)(x + 1) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + 1) equal to 18.466185313 and -18.466185313.Subproblem 1
x + 1 = 18.466185313 Simplifying x + 1 = 18.466185313 Reorder the terms: 1 + x = 18.466185313 Solving 1 + x = 18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 18.466185313 + -1 Combine like terms: 1 + -1 = 0 0 + x = 18.466185313 + -1 x = 18.466185313 + -1 Combine like terms: 18.466185313 + -1 = 17.466185313 x = 17.466185313 Simplifying x = 17.466185313Subproblem 2
x + 1 = -18.466185313 Simplifying x + 1 = -18.466185313 Reorder the terms: 1 + x = -18.466185313 Solving 1 + x = -18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -18.466185313 + -1 Combine like terms: 1 + -1 = 0 0 + x = -18.466185313 + -1 x = -18.466185313 + -1 Combine like terms: -18.466185313 + -1 = -19.466185313 x = -19.466185313 Simplifying x = -19.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.466185313, -19.466185313}Solution
x = {17.466185313, -19.466185313}
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