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Simplifying 39x2 + -478x + -2460 = 0 Reorder the terms: -2460 + -478x + 39x2 = 0 Solving -2460 + -478x + 39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. -63.07692308 + -12.25641026x + x2 = 0 Move the constant term to the right: Add '63.07692308' to each side of the equation. -63.07692308 + -12.25641026x + 63.07692308 + x2 = 0 + 63.07692308 Reorder the terms: -63.07692308 + 63.07692308 + -12.25641026x + x2 = 0 + 63.07692308 Combine like terms: -63.07692308 + 63.07692308 = 0.00000000 0.00000000 + -12.25641026x + x2 = 0 + 63.07692308 -12.25641026x + x2 = 0 + 63.07692308 Combine like terms: 0 + 63.07692308 = 63.07692308 -12.25641026x + x2 = 63.07692308 The x term is -12.25641026x. Take half its coefficient (-6.12820513). Square it (37.55489812) and add it to both sides. Add '37.55489812' to each side of the equation. -12.25641026x + 37.55489812 + x2 = 63.07692308 + 37.55489812 Reorder the terms: 37.55489812 + -12.25641026x + x2 = 63.07692308 + 37.55489812 Combine like terms: 63.07692308 + 37.55489812 = 100.6318212 37.55489812 + -12.25641026x + x2 = 100.6318212 Factor a perfect square on the left side: (x + -6.12820513)(x + -6.12820513) = 100.6318212 Calculate the square root of the right side: 10.031541317 Break this problem into two subproblems by setting (x + -6.12820513) equal to 10.031541317 and -10.031541317.Subproblem 1
x + -6.12820513 = 10.031541317 Simplifying x + -6.12820513 = 10.031541317 Reorder the terms: -6.12820513 + x = 10.031541317 Solving -6.12820513 + x = 10.031541317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12820513' to each side of the equation. -6.12820513 + 6.12820513 + x = 10.031541317 + 6.12820513 Combine like terms: -6.12820513 + 6.12820513 = 0.00000000 0.00000000 + x = 10.031541317 + 6.12820513 x = 10.031541317 + 6.12820513 Combine like terms: 10.031541317 + 6.12820513 = 16.159746447 x = 16.159746447 Simplifying x = 16.159746447Subproblem 2
x + -6.12820513 = -10.031541317 Simplifying x + -6.12820513 = -10.031541317 Reorder the terms: -6.12820513 + x = -10.031541317 Solving -6.12820513 + x = -10.031541317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.12820513' to each side of the equation. -6.12820513 + 6.12820513 + x = -10.031541317 + 6.12820513 Combine like terms: -6.12820513 + 6.12820513 = 0.00000000 0.00000000 + x = -10.031541317 + 6.12820513 x = -10.031541317 + 6.12820513 Combine like terms: -10.031541317 + 6.12820513 = -3.903336187 x = -3.903336187 Simplifying x = -3.903336187Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.159746447, -3.903336187}
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