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Simplifying 0 = 39x2 + -478x + -2463 Reorder the terms: 0 = -2463 + -478x + 39x2 Solving 0 = -2463 + -478x + 39x2 Solving for variable 'x'. Combine like terms: 0 + 2463 = 2463 2463 + 478x + -39x2 = -2463 + -478x + 39x2 + 2463 + 478x + -39x2 Reorder the terms: 2463 + 478x + -39x2 = -2463 + 2463 + -478x + 478x + 39x2 + -39x2 Combine like terms: -2463 + 2463 = 0 2463 + 478x + -39x2 = 0 + -478x + 478x + 39x2 + -39x2 2463 + 478x + -39x2 = -478x + 478x + 39x2 + -39x2 Combine like terms: -478x + 478x = 0 2463 + 478x + -39x2 = 0 + 39x2 + -39x2 2463 + 478x + -39x2 = 39x2 + -39x2 Combine like terms: 39x2 + -39x2 = 0 2463 + 478x + -39x2 = 0 Begin completing the square. Divide all terms by -39 the coefficient of the squared term: Divide each side by '-39'. -63.15384615 + -12.25641026x + x2 = 0 Move the constant term to the right: Add '63.15384615' to each side of the equation. -63.15384615 + -12.25641026x + 63.15384615 + x2 = 0 + 63.15384615 Reorder the terms: -63.15384615 + 63.15384615 + -12.25641026x + x2 = 0 + 63.15384615 Combine like terms: -63.15384615 + 63.15384615 = 0.00000000 0.00000000 + -12.25641026x + x2 = 0 + 63.15384615 -12.25641026x + x2 = 0 + 63.15384615 Combine like terms: 0 + 63.15384615 = 63.15384615 -12.25641026x + x2 = 63.15384615 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 = 63.15384615 + 37.55489812 Reorder the terms: 37.55489812 + -12.25641026x + x2 = 63.15384615 + 37.55489812 Combine like terms: 63.15384615 + 37.55489812 = 100.70874427 37.55489812 + -12.25641026x + x2 = 100.70874427 Factor a perfect square on the left side: (x + -6.12820513)(x + -6.12820513) = 100.70874427 Calculate the square root of the right side: 10.035374645 Break this problem into two subproblems by setting (x + -6.12820513) equal to 10.035374645 and -10.035374645.Subproblem 1
x + -6.12820513 = 10.035374645 Simplifying x + -6.12820513 = 10.035374645 Reorder the terms: -6.12820513 + x = 10.035374645 Solving -6.12820513 + x = 10.035374645 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 = 10.035374645 + 6.12820513 Combine like terms: -6.12820513 + 6.12820513 = 0.00000000 0.00000000 + x = 10.035374645 + 6.12820513 x = 10.035374645 + 6.12820513 Combine like terms: 10.035374645 + 6.12820513 = 16.163579775 x = 16.163579775 Simplifying x = 16.163579775Subproblem 2
x + -6.12820513 = -10.035374645 Simplifying x + -6.12820513 = -10.035374645 Reorder the terms: -6.12820513 + x = -10.035374645 Solving -6.12820513 + x = -10.035374645 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 = -10.035374645 + 6.12820513 Combine like terms: -6.12820513 + 6.12820513 = 0.00000000 0.00000000 + x = -10.035374645 + 6.12820513 x = -10.035374645 + 6.12820513 Combine like terms: -10.035374645 + 6.12820513 = -3.907169515 x = -3.907169515 Simplifying x = -3.907169515Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.163579775, -3.907169515}
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