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Simplifying 800 = 1.7x2 + 6x Reorder the terms: 800 = 6x + 1.7x2 Solving 800 = 6x + 1.7x2 Solving for variable 'x'. Reorder the terms: 800 + -6x + -1.7x2 = 6x + -6x + 1.7x2 + -1.7x2 Combine like terms: 6x + -6x = 0 800 + -6x + -1.7x2 = 0 + 1.7x2 + -1.7x2 800 + -6x + -1.7x2 = 1.7x2 + -1.7x2 Combine like terms: 1.7x2 + -1.7x2 = 0.0 800 + -6x + -1.7x2 = 0.0 Begin completing the square. Divide all terms by -1.7 the coefficient of the squared term: Divide each side by '-1.7'. -470.5882353 + 3.529411765x + x2 = 0 Move the constant term to the right: Add '470.5882353' to each side of the equation. -470.5882353 + 3.529411765x + 470.5882353 + x2 = 0 + 470.5882353 Reorder the terms: -470.5882353 + 470.5882353 + 3.529411765x + x2 = 0 + 470.5882353 Combine like terms: -470.5882353 + 470.5882353 = 0.0000000 0.0000000 + 3.529411765x + x2 = 0 + 470.5882353 3.529411765x + x2 = 0 + 470.5882353 Combine like terms: 0 + 470.5882353 = 470.5882353 3.529411765x + x2 = 470.5882353 The x term is 3.529411765x. Take half its coefficient (1.764705883). Square it (3.114186853) and add it to both sides. Add '3.114186853' to each side of the equation. 3.529411765x + 3.114186853 + x2 = 470.5882353 + 3.114186853 Reorder the terms: 3.114186853 + 3.529411765x + x2 = 470.5882353 + 3.114186853 Combine like terms: 470.5882353 + 3.114186853 = 473.702422153 3.114186853 + 3.529411765x + x2 = 473.702422153 Factor a perfect square on the left side: (x + 1.764705883)(x + 1.764705883) = 473.702422153 Calculate the square root of the right side: 21.764705883 Break this problem into two subproblems by setting (x + 1.764705883) equal to 21.764705883 and -21.764705883.Subproblem 1
x + 1.764705883 = 21.764705883 Simplifying x + 1.764705883 = 21.764705883 Reorder the terms: 1.764705883 + x = 21.764705883 Solving 1.764705883 + x = 21.764705883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.764705883' to each side of the equation. 1.764705883 + -1.764705883 + x = 21.764705883 + -1.764705883 Combine like terms: 1.764705883 + -1.764705883 = 0.000000000 0.000000000 + x = 21.764705883 + -1.764705883 x = 21.764705883 + -1.764705883 Combine like terms: 21.764705883 + -1.764705883 = 20 x = 20 Simplifying x = 20Subproblem 2
x + 1.764705883 = -21.764705883 Simplifying x + 1.764705883 = -21.764705883 Reorder the terms: 1.764705883 + x = -21.764705883 Solving 1.764705883 + x = -21.764705883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.764705883' to each side of the equation. 1.764705883 + -1.764705883 + x = -21.764705883 + -1.764705883 Combine like terms: 1.764705883 + -1.764705883 = 0.000000000 0.000000000 + x = -21.764705883 + -1.764705883 x = -21.764705883 + -1.764705883 Combine like terms: -21.764705883 + -1.764705883 = -23.529411766 x = -23.529411766 Simplifying x = -23.529411766Solution
The solution to the problem is based on the solutions from the subproblems. x = {20, -23.529411766}
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