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Simplifying -1x2 + 4x + 2 = -1(0.8333) * x + 7.81 Reorder the terms: 2 + 4x + -1x2 = -1(0.8333) * x + 7.81 Multiply -1 * 0.8333 2 + 4x + -1x2 = -0.8333x + 7.81 Reorder the terms: 2 + 4x + -1x2 = 7.81 + -0.8333x Solving 2 + 4x + -1x2 = 7.81 + -0.8333x Solving for variable 'x'. Reorder the terms: 2 + -7.81 + 4x + 0.8333x + -1x2 = 7.81 + -0.8333x + -7.81 + 0.8333x Combine like terms: 2 + -7.81 = -5.81 -5.81 + 4x + 0.8333x + -1x2 = 7.81 + -0.8333x + -7.81 + 0.8333x Combine like terms: 4x + 0.8333x = 4.8333x -5.81 + 4.8333x + -1x2 = 7.81 + -0.8333x + -7.81 + 0.8333x Reorder the terms: -5.81 + 4.8333x + -1x2 = 7.81 + -7.81 + -0.8333x + 0.8333x Combine like terms: 7.81 + -7.81 = 0.00 -5.81 + 4.8333x + -1x2 = 0.00 + -0.8333x + 0.8333x -5.81 + 4.8333x + -1x2 = -0.8333x + 0.8333x Combine like terms: -0.8333x + 0.8333x = 0.0000 -5.81 + 4.8333x + -1x2 = 0.0000 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5.81 + -4.8333x + x2 = 0.0000 Move the constant term to the right: Add '-5.81' to each side of the equation. 5.81 + -4.8333x + -5.81 + x2 = 0.0000 + -5.81 Reorder the terms: 5.81 + -5.81 + -4.8333x + x2 = 0.0000 + -5.81 Combine like terms: 5.81 + -5.81 = 0.00 0.00 + -4.8333x + x2 = 0.0000 + -5.81 -4.8333x + x2 = 0.0000 + -5.81 Combine like terms: 0.0000 + -5.81 = -5.81 -4.8333x + x2 = -5.81 The x term is -4.8333x. Take half its coefficient (-2.41665). Square it (5.840197223) and add it to both sides. Add '5.840197223' to each side of the equation. -4.8333x + 5.840197223 + x2 = -5.81 + 5.840197223 Reorder the terms: 5.840197223 + -4.8333x + x2 = -5.81 + 5.840197223 Combine like terms: -5.81 + 5.840197223 = 0.030197223 5.840197223 + -4.8333x + x2 = 0.030197223 Factor a perfect square on the left side: (x + -2.41665)(x + -2.41665) = 0.030197223 Calculate the square root of the right side: 0.173773482 Break this problem into two subproblems by setting (x + -2.41665) equal to 0.173773482 and -0.173773482.Subproblem 1
x + -2.41665 = 0.173773482 Simplifying x + -2.41665 = 0.173773482 Reorder the terms: -2.41665 + x = 0.173773482 Solving -2.41665 + x = 0.173773482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.41665' to each side of the equation. -2.41665 + 2.41665 + x = 0.173773482 + 2.41665 Combine like terms: -2.41665 + 2.41665 = 0.00000 0.00000 + x = 0.173773482 + 2.41665 x = 0.173773482 + 2.41665 Combine like terms: 0.173773482 + 2.41665 = 2.590423482 x = 2.590423482 Simplifying x = 2.590423482Subproblem 2
x + -2.41665 = -0.173773482 Simplifying x + -2.41665 = -0.173773482 Reorder the terms: -2.41665 + x = -0.173773482 Solving -2.41665 + x = -0.173773482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.41665' to each side of the equation. -2.41665 + 2.41665 + x = -0.173773482 + 2.41665 Combine like terms: -2.41665 + 2.41665 = 0.00000 0.00000 + x = -0.173773482 + 2.41665 x = -0.173773482 + 2.41665 Combine like terms: -0.173773482 + 2.41665 = 2.242876518 x = 2.242876518 Simplifying x = 2.242876518Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.590423482, 2.242876518}
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