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Simplifying 4x2 + 100x + -1200 = 0 Reorder the terms: -1200 + 100x + 4x2 = 0 Solving -1200 + 100x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-300 + 25x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-300 + 25x + x2)' equal to zero and attempt to solve: Simplifying -300 + 25x + x2 = 0 Solving -300 + 25x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 25x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 25x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 25x + x2 = 0 + 300 25x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 25x + x2 = 300 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 300 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 300 + 156.25 Combine like terms: 300 + 156.25 = 456.25 156.25 + 25x + x2 = 456.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 456.25 Calculate the square root of the right side: 21.360009363 Break this problem into two subproblems by setting (x + 12.5) equal to 21.360009363 and -21.360009363.Subproblem 1
x + 12.5 = 21.360009363 Simplifying x + 12.5 = 21.360009363 Reorder the terms: 12.5 + x = 21.360009363 Solving 12.5 + x = 21.360009363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 21.360009363 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 21.360009363 + -12.5 x = 21.360009363 + -12.5 Combine like terms: 21.360009363 + -12.5 = 8.860009363 x = 8.860009363 Simplifying x = 8.860009363Subproblem 2
x + 12.5 = -21.360009363 Simplifying x + 12.5 = -21.360009363 Reorder the terms: 12.5 + x = -21.360009363 Solving 12.5 + x = -21.360009363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -21.360009363 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -21.360009363 + -12.5 x = -21.360009363 + -12.5 Combine like terms: -21.360009363 + -12.5 = -33.860009363 x = -33.860009363 Simplifying x = -33.860009363Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.860009363, -33.860009363}Solution
x = {8.860009363, -33.860009363}
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