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Simplifying 100x2 + 400x + -8000 = 0 Reorder the terms: -8000 + 400x + 100x2 = 0 Solving -8000 + 400x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '100'. 100(-80 + 4x + x2) = 0 Ignore the factor 100.Subproblem 1
Set the factor '(-80 + 4x + x2)' equal to zero and attempt to solve: Simplifying -80 + 4x + x2 = 0 Solving -80 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + 4x + 80 + x2 = 0 + 80 Reorder the terms: -80 + 80 + 4x + x2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + 4x + x2 = 0 + 80 4x + x2 = 0 + 80 Combine like terms: 0 + 80 = 80 4x + x2 = 80 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 80 + 4 Reorder the terms: 4 + 4x + x2 = 80 + 4 Combine like terms: 80 + 4 = 84 4 + 4x + x2 = 84 Factor a perfect square on the left side: (x + 2)(x + 2) = 84 Calculate the square root of the right side: 9.16515139 Break this problem into two subproblems by setting (x + 2) equal to 9.16515139 and -9.16515139.Subproblem 1
x + 2 = 9.16515139 Simplifying x + 2 = 9.16515139 Reorder the terms: 2 + x = 9.16515139 Solving 2 + x = 9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.16515139 + -2 x = 9.16515139 + -2 Combine like terms: 9.16515139 + -2 = 7.16515139 x = 7.16515139 Simplifying x = 7.16515139Subproblem 2
x + 2 = -9.16515139 Simplifying x + 2 = -9.16515139 Reorder the terms: 2 + x = -9.16515139 Solving 2 + x = -9.16515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -9.16515139 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.16515139 + -2 x = -9.16515139 + -2 Combine like terms: -9.16515139 + -2 = -11.16515139 x = -11.16515139 Simplifying x = -11.16515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.16515139, -11.16515139}Solution
x = {7.16515139, -11.16515139}
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