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Simplifying 2x2 + 8x = 320 Reorder the terms: 8x + 2x2 = 320 Solving 8x + 2x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + 8x + 2x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -320 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-160 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-160 + 4x + x2)' equal to zero and attempt to solve: Simplifying -160 + 4x + x2 = 0 Solving -160 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '160' to each side of the equation. -160 + 4x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 4x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 4x + x2 = 0 + 160 4x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 4x + x2 = 160 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 = 160 + 4 Reorder the terms: 4 + 4x + x2 = 160 + 4 Combine like terms: 160 + 4 = 164 4 + 4x + x2 = 164 Factor a perfect square on the left side: (x + 2)(x + 2) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (x + 2) equal to 12.806248475 and -12.806248475.Subproblem 1
x + 2 = 12.806248475 Simplifying x + 2 = 12.806248475 Reorder the terms: 2 + x = 12.806248475 Solving 2 + x = 12.806248475 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 = 12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.806248475 + -2 x = 12.806248475 + -2 Combine like terms: 12.806248475 + -2 = 10.806248475 x = 10.806248475 Simplifying x = 10.806248475Subproblem 2
x + 2 = -12.806248475 Simplifying x + 2 = -12.806248475 Reorder the terms: 2 + x = -12.806248475 Solving 2 + x = -12.806248475 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 = -12.806248475 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.806248475 + -2 x = -12.806248475 + -2 Combine like terms: -12.806248475 + -2 = -14.806248475 x = -14.806248475 Simplifying x = -14.806248475Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.806248475, -14.806248475}Solution
x = {10.806248475, -14.806248475}
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