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Simplifying 63x2 + 64x + -100 = 0 Reorder the terms: -100 + 64x + 63x2 = 0 Solving -100 + 64x + 63x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -1.587301587 + 1.015873016x + x2 = 0 Move the constant term to the right: Add '1.587301587' to each side of the equation. -1.587301587 + 1.015873016x + 1.587301587 + x2 = 0 + 1.587301587 Reorder the terms: -1.587301587 + 1.587301587 + 1.015873016x + x2 = 0 + 1.587301587 Combine like terms: -1.587301587 + 1.587301587 = 0.000000000 0.000000000 + 1.015873016x + x2 = 0 + 1.587301587 1.015873016x + x2 = 0 + 1.587301587 Combine like terms: 0 + 1.587301587 = 1.587301587 1.015873016x + x2 = 1.587301587 The x term is 1.015873016x. Take half its coefficient (0.507936508). Square it (0.2579994962) and add it to both sides. Add '0.2579994962' to each side of the equation. 1.015873016x + 0.2579994962 + x2 = 1.587301587 + 0.2579994962 Reorder the terms: 0.2579994962 + 1.015873016x + x2 = 1.587301587 + 0.2579994962 Combine like terms: 1.587301587 + 0.2579994962 = 1.8453010832 0.2579994962 + 1.015873016x + x2 = 1.8453010832 Factor a perfect square on the left side: (x + 0.507936508)(x + 0.507936508) = 1.8453010832 Calculate the square root of the right side: 1.358418596 Break this problem into two subproblems by setting (x + 0.507936508) equal to 1.358418596 and -1.358418596.Subproblem 1
x + 0.507936508 = 1.358418596 Simplifying x + 0.507936508 = 1.358418596 Reorder the terms: 0.507936508 + x = 1.358418596 Solving 0.507936508 + x = 1.358418596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.507936508' to each side of the equation. 0.507936508 + -0.507936508 + x = 1.358418596 + -0.507936508 Combine like terms: 0.507936508 + -0.507936508 = 0.000000000 0.000000000 + x = 1.358418596 + -0.507936508 x = 1.358418596 + -0.507936508 Combine like terms: 1.358418596 + -0.507936508 = 0.850482088 x = 0.850482088 Simplifying x = 0.850482088Subproblem 2
x + 0.507936508 = -1.358418596 Simplifying x + 0.507936508 = -1.358418596 Reorder the terms: 0.507936508 + x = -1.358418596 Solving 0.507936508 + x = -1.358418596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.507936508' to each side of the equation. 0.507936508 + -0.507936508 + x = -1.358418596 + -0.507936508 Combine like terms: 0.507936508 + -0.507936508 = 0.000000000 0.000000000 + x = -1.358418596 + -0.507936508 x = -1.358418596 + -0.507936508 Combine like terms: -1.358418596 + -0.507936508 = -1.866355104 x = -1.866355104 Simplifying x = -1.866355104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.850482088, -1.866355104}
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