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Simplifying 6.75x2 + -170x + 800 = 0 Reorder the terms: 800 + -170x + 6.75x2 = 0 Solving 800 + -170x + 6.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.75 the coefficient of the squared term: Divide each side by '6.75'. 118.5185185 + -25.18518519x + x2 = 0 Move the constant term to the right: Add '-118.5185185' to each side of the equation. 118.5185185 + -25.18518519x + -118.5185185 + x2 = 0 + -118.5185185 Reorder the terms: 118.5185185 + -118.5185185 + -25.18518519x + x2 = 0 + -118.5185185 Combine like terms: 118.5185185 + -118.5185185 = 0.0000000 0.0000000 + -25.18518519x + x2 = 0 + -118.5185185 -25.18518519x + x2 = 0 + -118.5185185 Combine like terms: 0 + -118.5185185 = -118.5185185 -25.18518519x + x2 = -118.5185185 The x term is -25.18518519x. Take half its coefficient (-12.5925926). Square it (158.5733884) and add it to both sides. Add '158.5733884' to each side of the equation. -25.18518519x + 158.5733884 + x2 = -118.5185185 + 158.5733884 Reorder the terms: 158.5733884 + -25.18518519x + x2 = -118.5185185 + 158.5733884 Combine like terms: -118.5185185 + 158.5733884 = 40.0548699 158.5733884 + -25.18518519x + x2 = 40.0548699 Factor a perfect square on the left side: (x + -12.5925926)(x + -12.5925926) = 40.0548699 Calculate the square root of the right side: 6.32889168 Break this problem into two subproblems by setting (x + -12.5925926) equal to 6.32889168 and -6.32889168.Subproblem 1
x + -12.5925926 = 6.32889168 Simplifying x + -12.5925926 = 6.32889168 Reorder the terms: -12.5925926 + x = 6.32889168 Solving -12.5925926 + x = 6.32889168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5925926' to each side of the equation. -12.5925926 + 12.5925926 + x = 6.32889168 + 12.5925926 Combine like terms: -12.5925926 + 12.5925926 = 0.0000000 0.0000000 + x = 6.32889168 + 12.5925926 x = 6.32889168 + 12.5925926 Combine like terms: 6.32889168 + 12.5925926 = 18.92148428 x = 18.92148428 Simplifying x = 18.92148428Subproblem 2
x + -12.5925926 = -6.32889168 Simplifying x + -12.5925926 = -6.32889168 Reorder the terms: -12.5925926 + x = -6.32889168 Solving -12.5925926 + x = -6.32889168 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5925926' to each side of the equation. -12.5925926 + 12.5925926 + x = -6.32889168 + 12.5925926 Combine like terms: -12.5925926 + 12.5925926 = 0.0000000 0.0000000 + x = -6.32889168 + 12.5925926 x = -6.32889168 + 12.5925926 Combine like terms: -6.32889168 + 12.5925926 = 6.26370092 x = 6.26370092 Simplifying x = 6.26370092Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.92148428, 6.26370092}
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