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Simplifying (63x2) + -1(60x) + -1 = 0 Remove parenthesis around (60x) (63x2) + -1 * 60x + -1 = 0 Multiply -1 * 60 (63x2) + -60x + -1 = 0 Reorder the terms: -1 + -60x + (63x2) = 0 Solving -1 + -60x + (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'. -0.01587301587 + -0.9523809524x + x2 = 0 Move the constant term to the right: Add '0.01587301587' to each side of the equation. -0.01587301587 + -0.9523809524x + 0.01587301587 + x2 = 0 + 0.01587301587 Reorder the terms: -0.01587301587 + 0.01587301587 + -0.9523809524x + x2 = 0 + 0.01587301587 Combine like terms: -0.01587301587 + 0.01587301587 = 0.00000000000 0.00000000000 + -0.9523809524x + x2 = 0 + 0.01587301587 -0.9523809524x + x2 = 0 + 0.01587301587 Combine like terms: 0 + 0.01587301587 = 0.01587301587 -0.9523809524x + x2 = 0.01587301587 The x term is -0.9523809524x. Take half its coefficient (-0.4761904762). Square it (0.2267573696) and add it to both sides. Add '0.2267573696' to each side of the equation. -0.9523809524x + 0.2267573696 + x2 = 0.01587301587 + 0.2267573696 Reorder the terms: 0.2267573696 + -0.9523809524x + x2 = 0.01587301587 + 0.2267573696 Combine like terms: 0.01587301587 + 0.2267573696 = 0.24263038547 0.2267573696 + -0.9523809524x + x2 = 0.24263038547 Factor a perfect square on the left side: ((x) + -0.4761904762)((x) + -0.4761904762) = 0.24263038547 Calculate the square root of the right side: 0.492575259 Break this problem into two subproblems by setting ((x) + -0.4761904762) equal to 0.492575259 and -0.492575259.Subproblem 1
(x) + -0.4761904762 = 0.492575259 Simplifying (x) + -0.4761904762 = 0.492575259 x + -0.4761904762 = 0.492575259 Reorder the terms: -0.4761904762 + x = 0.492575259 Solving -0.4761904762 + x = 0.492575259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = 0.492575259 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = 0.492575259 + 0.4761904762 x = 0.492575259 + 0.4761904762 Combine like terms: 0.492575259 + 0.4761904762 = 0.9687657352 x = 0.9687657352 Simplifying x = 0.9687657352Subproblem 2
(x) + -0.4761904762 = -0.492575259 Simplifying (x) + -0.4761904762 = -0.492575259 x + -0.4761904762 = -0.492575259 Reorder the terms: -0.4761904762 + x = -0.492575259 Solving -0.4761904762 + x = -0.492575259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = -0.492575259 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = -0.492575259 + 0.4761904762 x = -0.492575259 + 0.4761904762 Combine like terms: -0.492575259 + 0.4761904762 = -0.0163847828 x = -0.0163847828 Simplifying x = -0.0163847828Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9687657352, -0.0163847828}
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