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Simplifying -0.215x2 + 171.48x + 16668.735 = 0 Reorder the terms: 16668.735 + 171.48x + -0.215x2 = 0 Solving 16668.735 + 171.48x + -0.215x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.215 the coefficient of the squared term: Divide each side by '-0.215'. -77529 + -797.5813953x + x2 = 0 Move the constant term to the right: Add '77529' to each side of the equation. -77529 + -797.5813953x + 77529 + x2 = 0 + 77529 Reorder the terms: -77529 + 77529 + -797.5813953x + x2 = 0 + 77529 Combine like terms: -77529 + 77529 = 0 0 + -797.5813953x + x2 = 0 + 77529 -797.5813953x + x2 = 0 + 77529 Combine like terms: 0 + 77529 = 77529 -797.5813953x + x2 = 77529 The x term is -797.5813953x. Take half its coefficient (-398.7906977). Square it (159034.0206) and add it to both sides. Add '159034.0206' to each side of the equation. -797.5813953x + 159034.0206 + x2 = 77529 + 159034.0206 Reorder the terms: 159034.0206 + -797.5813953x + x2 = 77529 + 159034.0206 Combine like terms: 77529 + 159034.0206 = 236563.0206 159034.0206 + -797.5813953x + x2 = 236563.0206 Factor a perfect square on the left side: (x + -398.7906977)(x + -398.7906977) = 236563.0206 Calculate the square root of the right side: 486.37744664 Break this problem into two subproblems by setting (x + -398.7906977) equal to 486.37744664 and -486.37744664.Subproblem 1
x + -398.7906977 = 486.37744664 Simplifying x + -398.7906977 = 486.37744664 Reorder the terms: -398.7906977 + x = 486.37744664 Solving -398.7906977 + x = 486.37744664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '398.7906977' to each side of the equation. -398.7906977 + 398.7906977 + x = 486.37744664 + 398.7906977 Combine like terms: -398.7906977 + 398.7906977 = 0.0000000 0.0000000 + x = 486.37744664 + 398.7906977 x = 486.37744664 + 398.7906977 Combine like terms: 486.37744664 + 398.7906977 = 885.16814434 x = 885.16814434 Simplifying x = 885.16814434Subproblem 2
x + -398.7906977 = -486.37744664 Simplifying x + -398.7906977 = -486.37744664 Reorder the terms: -398.7906977 + x = -486.37744664 Solving -398.7906977 + x = -486.37744664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '398.7906977' to each side of the equation. -398.7906977 + 398.7906977 + x = -486.37744664 + 398.7906977 Combine like terms: -398.7906977 + 398.7906977 = 0.0000000 0.0000000 + x = -486.37744664 + 398.7906977 x = -486.37744664 + 398.7906977 Combine like terms: -486.37744664 + 398.7906977 = -87.58674894 x = -87.58674894 Simplifying x = -87.58674894Solution
The solution to the problem is based on the solutions from the subproblems. x = {885.16814434, -87.58674894}
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