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Simplifying 2x2 + 20x = 6300 Reorder the terms: 20x + 2x2 = 6300 Solving 20x + 2x2 = 6300 Solving for variable 'x'. Reorder the terms: -6300 + 20x + 2x2 = 6300 + -6300 Combine like terms: 6300 + -6300 = 0 -6300 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3150 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3150 + 10x + x2)' equal to zero and attempt to solve: Simplifying -3150 + 10x + x2 = 0 Solving -3150 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3150' to each side of the equation. -3150 + 10x + 3150 + x2 = 0 + 3150 Reorder the terms: -3150 + 3150 + 10x + x2 = 0 + 3150 Combine like terms: -3150 + 3150 = 0 0 + 10x + x2 = 0 + 3150 10x + x2 = 0 + 3150 Combine like terms: 0 + 3150 = 3150 10x + x2 = 3150 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 3150 + 25 Reorder the terms: 25 + 10x + x2 = 3150 + 25 Combine like terms: 3150 + 25 = 3175 25 + 10x + x2 = 3175 Factor a perfect square on the left side: (x + 5)(x + 5) = 3175 Calculate the square root of the right side: 56.347138348 Break this problem into two subproblems by setting (x + 5) equal to 56.347138348 and -56.347138348.Subproblem 1
x + 5 = 56.347138348 Simplifying x + 5 = 56.347138348 Reorder the terms: 5 + x = 56.347138348 Solving 5 + x = 56.347138348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 56.347138348 + -5 Combine like terms: 5 + -5 = 0 0 + x = 56.347138348 + -5 x = 56.347138348 + -5 Combine like terms: 56.347138348 + -5 = 51.347138348 x = 51.347138348 Simplifying x = 51.347138348Subproblem 2
x + 5 = -56.347138348 Simplifying x + 5 = -56.347138348 Reorder the terms: 5 + x = -56.347138348 Solving 5 + x = -56.347138348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -56.347138348 + -5 Combine like terms: 5 + -5 = 0 0 + x = -56.347138348 + -5 x = -56.347138348 + -5 Combine like terms: -56.347138348 + -5 = -61.347138348 x = -61.347138348 Simplifying x = -61.347138348Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.347138348, -61.347138348}Solution
x = {51.347138348, -61.347138348}
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