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Simplifying 0 = -6.86x + 4x2 + 0.41 Reorder the terms: 0 = 0.41 + -6.86x + 4x2 Solving 0 = 0.41 + -6.86x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -0.41 = -0.41 -0.41 + 6.86x + -4x2 = 0.41 + -6.86x + 4x2 + -0.41 + 6.86x + -4x2 Reorder the terms: -0.41 + 6.86x + -4x2 = 0.41 + -0.41 + -6.86x + 6.86x + 4x2 + -4x2 Combine like terms: 0.41 + -0.41 = 0.00 -0.41 + 6.86x + -4x2 = 0.00 + -6.86x + 6.86x + 4x2 + -4x2 -0.41 + 6.86x + -4x2 = -6.86x + 6.86x + 4x2 + -4x2 Combine like terms: -6.86x + 6.86x = 0.00 -0.41 + 6.86x + -4x2 = 0.00 + 4x2 + -4x2 -0.41 + 6.86x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -0.41 + 6.86x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.1025 + -1.715x + x2 = 0 Move the constant term to the right: Add '-0.1025' to each side of the equation. 0.1025 + -1.715x + -0.1025 + x2 = 0 + -0.1025 Reorder the terms: 0.1025 + -0.1025 + -1.715x + x2 = 0 + -0.1025 Combine like terms: 0.1025 + -0.1025 = 0.0000 0.0000 + -1.715x + x2 = 0 + -0.1025 -1.715x + x2 = 0 + -0.1025 Combine like terms: 0 + -0.1025 = -0.1025 -1.715x + x2 = -0.1025 The x term is -1.715x. Take half its coefficient (-0.8575). Square it (0.73530625) and add it to both sides. Add '0.73530625' to each side of the equation. -1.715x + 0.73530625 + x2 = -0.1025 + 0.73530625 Reorder the terms: 0.73530625 + -1.715x + x2 = -0.1025 + 0.73530625 Combine like terms: -0.1025 + 0.73530625 = 0.63280625 0.73530625 + -1.715x + x2 = 0.63280625 Factor a perfect square on the left side: (x + -0.8575)(x + -0.8575) = 0.63280625 Calculate the square root of the right side: 0.7954912 Break this problem into two subproblems by setting (x + -0.8575) equal to 0.7954912 and -0.7954912.Subproblem 1
x + -0.8575 = 0.7954912 Simplifying x + -0.8575 = 0.7954912 Reorder the terms: -0.8575 + x = 0.7954912 Solving -0.8575 + x = 0.7954912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8575' to each side of the equation. -0.8575 + 0.8575 + x = 0.7954912 + 0.8575 Combine like terms: -0.8575 + 0.8575 = 0.0000 0.0000 + x = 0.7954912 + 0.8575 x = 0.7954912 + 0.8575 Combine like terms: 0.7954912 + 0.8575 = 1.6529912 x = 1.6529912 Simplifying x = 1.6529912Subproblem 2
x + -0.8575 = -0.7954912 Simplifying x + -0.8575 = -0.7954912 Reorder the terms: -0.8575 + x = -0.7954912 Solving -0.8575 + x = -0.7954912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8575' to each side of the equation. -0.8575 + 0.8575 + x = -0.7954912 + 0.8575 Combine like terms: -0.8575 + 0.8575 = 0.0000 0.0000 + x = -0.7954912 + 0.8575 x = -0.7954912 + 0.8575 Combine like terms: -0.7954912 + 0.8575 = 0.0620088 x = 0.0620088 Simplifying x = 0.0620088Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6529912, 0.0620088}
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