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Simplifying 25x * x + 400x = 58000 Multiply x * x 25x2 + 400x = 58000 Reorder the terms: 400x + 25x2 = 58000 Solving 400x + 25x2 = 58000 Solving for variable 'x'. Reorder the terms: -58000 + 400x + 25x2 = 58000 + -58000 Combine like terms: 58000 + -58000 = 0 -58000 + 400x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-2320 + 16x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-2320 + 16x + x2)' equal to zero and attempt to solve: Simplifying -2320 + 16x + x2 = 0 Solving -2320 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2320' to each side of the equation. -2320 + 16x + 2320 + x2 = 0 + 2320 Reorder the terms: -2320 + 2320 + 16x + x2 = 0 + 2320 Combine like terms: -2320 + 2320 = 0 0 + 16x + x2 = 0 + 2320 16x + x2 = 0 + 2320 Combine like terms: 0 + 2320 = 2320 16x + x2 = 2320 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = 2320 + 64 Reorder the terms: 64 + 16x + x2 = 2320 + 64 Combine like terms: 2320 + 64 = 2384 64 + 16x + x2 = 2384 Factor a perfect square on the left side: (x + 8)(x + 8) = 2384 Calculate the square root of the right side: 48.826222463 Break this problem into two subproblems by setting (x + 8) equal to 48.826222463 and -48.826222463.Subproblem 1
x + 8 = 48.826222463 Simplifying x + 8 = 48.826222463 Reorder the terms: 8 + x = 48.826222463 Solving 8 + x = 48.826222463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 48.826222463 + -8 Combine like terms: 8 + -8 = 0 0 + x = 48.826222463 + -8 x = 48.826222463 + -8 Combine like terms: 48.826222463 + -8 = 40.826222463 x = 40.826222463 Simplifying x = 40.826222463Subproblem 2
x + 8 = -48.826222463 Simplifying x + 8 = -48.826222463 Reorder the terms: 8 + x = -48.826222463 Solving 8 + x = -48.826222463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -48.826222463 + -8 Combine like terms: 8 + -8 = 0 0 + x = -48.826222463 + -8 x = -48.826222463 + -8 Combine like terms: -48.826222463 + -8 = -56.826222463 x = -56.826222463 Simplifying x = -56.826222463Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.826222463, -56.826222463}Solution
x = {40.826222463, -56.826222463}
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