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Simplifying -1x2 + 4x + 2 = -0.83x + 7.81 Reorder the terms: 2 + 4x + -1x2 = -0.83x + 7.81 Reorder the terms: 2 + 4x + -1x2 = 7.81 + -0.83x Solving 2 + 4x + -1x2 = 7.81 + -0.83x Solving for variable 'x'. Reorder the terms: 2 + -7.81 + 4x + 0.83x + -1x2 = 7.81 + -0.83x + -7.81 + 0.83x Combine like terms: 2 + -7.81 = -5.81 -5.81 + 4x + 0.83x + -1x2 = 7.81 + -0.83x + -7.81 + 0.83x Combine like terms: 4x + 0.83x = 4.83x -5.81 + 4.83x + -1x2 = 7.81 + -0.83x + -7.81 + 0.83x Reorder the terms: -5.81 + 4.83x + -1x2 = 7.81 + -7.81 + -0.83x + 0.83x Combine like terms: 7.81 + -7.81 = 0.00 -5.81 + 4.83x + -1x2 = 0.00 + -0.83x + 0.83x -5.81 + 4.83x + -1x2 = -0.83x + 0.83x Combine like terms: -0.83x + 0.83x = 0.00 -5.81 + 4.83x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5.81 + -4.83x + x2 = 0.00 Move the constant term to the right: Add '-5.81' to each side of the equation. 5.81 + -4.83x + -5.81 + x2 = 0.00 + -5.81 Reorder the terms: 5.81 + -5.81 + -4.83x + x2 = 0.00 + -5.81 Combine like terms: 5.81 + -5.81 = 0.00 0.00 + -4.83x + x2 = 0.00 + -5.81 -4.83x + x2 = 0.00 + -5.81 Combine like terms: 0.00 + -5.81 = -5.81 -4.83x + x2 = -5.81 The x term is -4.83x. Take half its coefficient (-2.415). Square it (5.832225) and add it to both sides. Add '5.832225' to each side of the equation. -4.83x + 5.832225 + x2 = -5.81 + 5.832225 Reorder the terms: 5.832225 + -4.83x + x2 = -5.81 + 5.832225 Combine like terms: -5.81 + 5.832225 = 0.022225 5.832225 + -4.83x + x2 = 0.022225 Factor a perfect square on the left side: (x + -2.415)(x + -2.415) = 0.022225 Calculate the square root of the right side: 0.149080515 Break this problem into two subproblems by setting (x + -2.415) equal to 0.149080515 and -0.149080515.Subproblem 1
x + -2.415 = 0.149080515 Simplifying x + -2.415 = 0.149080515 Reorder the terms: -2.415 + x = 0.149080515 Solving -2.415 + x = 0.149080515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.415' to each side of the equation. -2.415 + 2.415 + x = 0.149080515 + 2.415 Combine like terms: -2.415 + 2.415 = 0.000 0.000 + x = 0.149080515 + 2.415 x = 0.149080515 + 2.415 Combine like terms: 0.149080515 + 2.415 = 2.564080515 x = 2.564080515 Simplifying x = 2.564080515Subproblem 2
x + -2.415 = -0.149080515 Simplifying x + -2.415 = -0.149080515 Reorder the terms: -2.415 + x = -0.149080515 Solving -2.415 + x = -0.149080515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.415' to each side of the equation. -2.415 + 2.415 + x = -0.149080515 + 2.415 Combine like terms: -2.415 + 2.415 = 0.000 0.000 + x = -0.149080515 + 2.415 x = -0.149080515 + 2.415 Combine like terms: -0.149080515 + 2.415 = 2.265919485 x = 2.265919485 Simplifying x = 2.265919485Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.564080515, 2.265919485}
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