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Simplifying 2x2 + 40x + -2100 = 0 Reorder the terms: -2100 + 40x + 2x2 = 0 Solving -2100 + 40x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1050 + 20x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1050 + 20x + x2)' equal to zero and attempt to solve: Simplifying -1050 + 20x + x2 = 0 Solving -1050 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1050' to each side of the equation. -1050 + 20x + 1050 + x2 = 0 + 1050 Reorder the terms: -1050 + 1050 + 20x + x2 = 0 + 1050 Combine like terms: -1050 + 1050 = 0 0 + 20x + x2 = 0 + 1050 20x + x2 = 0 + 1050 Combine like terms: 0 + 1050 = 1050 20x + x2 = 1050 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 1050 + 100 Reorder the terms: 100 + 20x + x2 = 1050 + 100 Combine like terms: 1050 + 100 = 1150 100 + 20x + x2 = 1150 Factor a perfect square on the left side: (x + 10)(x + 10) = 1150 Calculate the square root of the right side: 33.911649916 Break this problem into two subproblems by setting (x + 10) equal to 33.911649916 and -33.911649916.Subproblem 1
x + 10 = 33.911649916 Simplifying x + 10 = 33.911649916 Reorder the terms: 10 + x = 33.911649916 Solving 10 + x = 33.911649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 33.911649916 + -10 Combine like terms: 10 + -10 = 0 0 + x = 33.911649916 + -10 x = 33.911649916 + -10 Combine like terms: 33.911649916 + -10 = 23.911649916 x = 23.911649916 Simplifying x = 23.911649916Subproblem 2
x + 10 = -33.911649916 Simplifying x + 10 = -33.911649916 Reorder the terms: 10 + x = -33.911649916 Solving 10 + x = -33.911649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -33.911649916 + -10 Combine like terms: 10 + -10 = 0 0 + x = -33.911649916 + -10 x = -33.911649916 + -10 Combine like terms: -33.911649916 + -10 = -43.911649916 x = -43.911649916 Simplifying x = -43.911649916Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.911649916, -43.911649916}Solution
x = {23.911649916, -43.911649916}
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