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Simplifying 4x2 + 1120x + -201600 = 0 Reorder the terms: -201600 + 1120x + 4x2 = 0 Solving -201600 + 1120x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-50400 + 280x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50400 + 280x + x2)' equal to zero and attempt to solve: Simplifying -50400 + 280x + x2 = 0 Solving -50400 + 280x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50400' to each side of the equation. -50400 + 280x + 50400 + x2 = 0 + 50400 Reorder the terms: -50400 + 50400 + 280x + x2 = 0 + 50400 Combine like terms: -50400 + 50400 = 0 0 + 280x + x2 = 0 + 50400 280x + x2 = 0 + 50400 Combine like terms: 0 + 50400 = 50400 280x + x2 = 50400 The x term is 280x. Take half its coefficient (140). Square it (19600) and add it to both sides. Add '19600' to each side of the equation. 280x + 19600 + x2 = 50400 + 19600 Reorder the terms: 19600 + 280x + x2 = 50400 + 19600 Combine like terms: 50400 + 19600 = 70000 19600 + 280x + x2 = 70000 Factor a perfect square on the left side: (x + 140)(x + 140) = 70000 Calculate the square root of the right side: 264.575131106 Break this problem into two subproblems by setting (x + 140) equal to 264.575131106 and -264.575131106.Subproblem 1
x + 140 = 264.575131106 Simplifying x + 140 = 264.575131106 Reorder the terms: 140 + x = 264.575131106 Solving 140 + x = 264.575131106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = 264.575131106 + -140 Combine like terms: 140 + -140 = 0 0 + x = 264.575131106 + -140 x = 264.575131106 + -140 Combine like terms: 264.575131106 + -140 = 124.575131106 x = 124.575131106 Simplifying x = 124.575131106Subproblem 2
x + 140 = -264.575131106 Simplifying x + 140 = -264.575131106 Reorder the terms: 140 + x = -264.575131106 Solving 140 + x = -264.575131106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-140' to each side of the equation. 140 + -140 + x = -264.575131106 + -140 Combine like terms: 140 + -140 = 0 0 + x = -264.575131106 + -140 x = -264.575131106 + -140 Combine like terms: -264.575131106 + -140 = -404.575131106 x = -404.575131106 Simplifying x = -404.575131106Solution
The solution to the problem is based on the solutions from the subproblems. x = {124.575131106, -404.575131106}Solution
x = {124.575131106, -404.575131106}
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