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Simplifying 8.5x4 + -1161.875x2 + 24150 = 0 Reorder the terms: 24150 + -1161.875x2 + 8.5x4 = 0 Solving 24150 + -1161.875x2 + 8.5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8.5 the coefficient of the squared term: Divide each side by '8.5'. 2841.176471 + -136.6911765x2 + x4 = 0 Move the constant term to the right: Add '-2841.176471' to each side of the equation. 2841.176471 + -136.6911765x2 + -2841.176471 + x4 = 0 + -2841.176471 Reorder the terms: 2841.176471 + -2841.176471 + -136.6911765x2 + x4 = 0 + -2841.176471 Combine like terms: 2841.176471 + -2841.176471 = 0.000000 0.000000 + -136.6911765x2 + x4 = 0 + -2841.176471 -136.6911765x2 + x4 = 0 + -2841.176471 Combine like terms: 0 + -2841.176471 = -2841.176471 -136.6911765x2 + x4 = -2841.176471 The x term is -136.6911765x2. Take half its coefficient (-68.34558825). Square it (4671.119433) and add it to both sides. Add '4671.119433' to each side of the equation. -136.6911765x2 + 4671.119433 + x4 = -2841.176471 + 4671.119433 Reorder the terms: 4671.119433 + -136.6911765x2 + x4 = -2841.176471 + 4671.119433 Combine like terms: -2841.176471 + 4671.119433 = 1829.942962 4671.119433 + -136.6911765x2 + x4 = 1829.942962 Factor a perfect square on the left side: (x2 + -68.34558825)(x2 + -68.34558825) = 1829.942962 Calculate the square root of the right side: 42.777832601 Break this problem into two subproblems by setting (x2 + -68.34558825) equal to 42.777832601 and -42.777832601.Subproblem 1
x2 + -68.34558825 = 42.777832601 Simplifying x2 + -68.34558825 = 42.777832601 Reorder the terms: -68.34558825 + x2 = 42.777832601 Solving -68.34558825 + x2 = 42.777832601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.34558825' to each side of the equation. -68.34558825 + 68.34558825 + x2 = 42.777832601 + 68.34558825 Combine like terms: -68.34558825 + 68.34558825 = 0.00000000 0.00000000 + x2 = 42.777832601 + 68.34558825 x2 = 42.777832601 + 68.34558825 Combine like terms: 42.777832601 + 68.34558825 = 111.123420851 x2 = 111.123420851 Simplifying x2 = 111.123420851 Take the square root of each side: x = {-10.54150942, 10.54150942}Subproblem 2
x2 + -68.34558825 = -42.777832601 Simplifying x2 + -68.34558825 = -42.777832601 Reorder the terms: -68.34558825 + x2 = -42.777832601 Solving -68.34558825 + x2 = -42.777832601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.34558825' to each side of the equation. -68.34558825 + 68.34558825 + x2 = -42.777832601 + 68.34558825 Combine like terms: -68.34558825 + 68.34558825 = 0.00000000 0.00000000 + x2 = -42.777832601 + 68.34558825 x2 = -42.777832601 + 68.34558825 Combine like terms: -42.777832601 + 68.34558825 = 25.567755649 x2 = 25.567755649 Simplifying x2 = 25.567755649 Take the square root of each side: x = {-5.056456828, 5.056456828}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-10.54150942, 10.54150942, -5.056456828, 5.056456828}
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