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Simplifying 4x2 + 120x + 3600 = 9700 Reorder the terms: 3600 + 120x + 4x2 = 9700 Solving 3600 + 120x + 4x2 = 9700 Solving for variable 'x'. Reorder the terms: 3600 + -9700 + 120x + 4x2 = 9700 + -9700 Combine like terms: 3600 + -9700 = -6100 -6100 + 120x + 4x2 = 9700 + -9700 Combine like terms: 9700 + -9700 = 0 -6100 + 120x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1525 + 30x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1525 + 30x + x2)' equal to zero and attempt to solve: Simplifying -1525 + 30x + x2 = 0 Solving -1525 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1525' to each side of the equation. -1525 + 30x + 1525 + x2 = 0 + 1525 Reorder the terms: -1525 + 1525 + 30x + x2 = 0 + 1525 Combine like terms: -1525 + 1525 = 0 0 + 30x + x2 = 0 + 1525 30x + x2 = 0 + 1525 Combine like terms: 0 + 1525 = 1525 30x + x2 = 1525 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 1525 + 225 Reorder the terms: 225 + 30x + x2 = 1525 + 225 Combine like terms: 1525 + 225 = 1750 225 + 30x + x2 = 1750 Factor a perfect square on the left side: (x + 15)(x + 15) = 1750 Calculate the square root of the right side: 41.833001327 Break this problem into two subproblems by setting (x + 15) equal to 41.833001327 and -41.833001327.Subproblem 1
x + 15 = 41.833001327 Simplifying x + 15 = 41.833001327 Reorder the terms: 15 + x = 41.833001327 Solving 15 + x = 41.833001327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 41.833001327 + -15 Combine like terms: 15 + -15 = 0 0 + x = 41.833001327 + -15 x = 41.833001327 + -15 Combine like terms: 41.833001327 + -15 = 26.833001327 x = 26.833001327 Simplifying x = 26.833001327Subproblem 2
x + 15 = -41.833001327 Simplifying x + 15 = -41.833001327 Reorder the terms: 15 + x = -41.833001327 Solving 15 + x = -41.833001327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -41.833001327 + -15 Combine like terms: 15 + -15 = 0 0 + x = -41.833001327 + -15 x = -41.833001327 + -15 Combine like terms: -41.833001327 + -15 = -56.833001327 x = -56.833001327 Simplifying x = -56.833001327Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.833001327, -56.833001327}Solution
x = {26.833001327, -56.833001327}
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