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Simplifying 25x2 + 25x = 22500 Reorder the terms: 25x + 25x2 = 22500 Solving 25x + 25x2 = 22500 Solving for variable 'x'. Reorder the terms: -22500 + 25x + 25x2 = 22500 + -22500 Combine like terms: 22500 + -22500 = 0 -22500 + 25x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(-900 + x + x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(-900 + x + x2)' equal to zero and attempt to solve: Simplifying -900 + x + x2 = 0 Solving -900 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + x + x2 = 0 + 900 x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 x + x2 = 900 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 900 + 0.25 Reorder the terms: 0.25 + x + x2 = 900 + 0.25 Combine like terms: 900 + 0.25 = 900.25 0.25 + x + x2 = 900.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 900.25 Calculate the square root of the right side: 30.004166377 Break this problem into two subproblems by setting (x + 0.5) equal to 30.004166377 and -30.004166377.Subproblem 1
x + 0.5 = 30.004166377 Simplifying x + 0.5 = 30.004166377 Reorder the terms: 0.5 + x = 30.004166377 Solving 0.5 + x = 30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 30.004166377 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 30.004166377 + -0.5 x = 30.004166377 + -0.5 Combine like terms: 30.004166377 + -0.5 = 29.504166377 x = 29.504166377 Simplifying x = 29.504166377Subproblem 2
x + 0.5 = -30.004166377 Simplifying x + 0.5 = -30.004166377 Reorder the terms: 0.5 + x = -30.004166377 Solving 0.5 + x = -30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -30.004166377 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -30.004166377 + -0.5 x = -30.004166377 + -0.5 Combine like terms: -30.004166377 + -0.5 = -30.504166377 x = -30.504166377 Simplifying x = -30.504166377Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.504166377, -30.504166377}Solution
x = {29.504166377, -30.504166377}
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