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Simplifying -1x2 + 4x + 2 = -0.83x + -3.83 Reorder the terms: 2 + 4x + -1x2 = -0.83x + -3.83 Reorder the terms: 2 + 4x + -1x2 = -3.83 + -0.83x Solving 2 + 4x + -1x2 = -3.83 + -0.83x Solving for variable 'x'. Reorder the terms: 2 + 3.83 + 4x + 0.83x + -1x2 = -3.83 + -0.83x + 3.83 + 0.83x Combine like terms: 2 + 3.83 = 5.83 5.83 + 4x + 0.83x + -1x2 = -3.83 + -0.83x + 3.83 + 0.83x Combine like terms: 4x + 0.83x = 4.83x 5.83 + 4.83x + -1x2 = -3.83 + -0.83x + 3.83 + 0.83x Reorder the terms: 5.83 + 4.83x + -1x2 = -3.83 + 3.83 + -0.83x + 0.83x Combine like terms: -3.83 + 3.83 = 0.00 5.83 + 4.83x + -1x2 = 0.00 + -0.83x + 0.83x 5.83 + 4.83x + -1x2 = -0.83x + 0.83x Combine like terms: -0.83x + 0.83x = 0.00 5.83 + 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'. -5.83 + -4.83x + x2 = 0.00 Move the constant term to the right: Add '5.83' to each side of the equation. -5.83 + -4.83x + 5.83 + x2 = 0.00 + 5.83 Reorder the terms: -5.83 + 5.83 + -4.83x + x2 = 0.00 + 5.83 Combine like terms: -5.83 + 5.83 = 0.00 0.00 + -4.83x + x2 = 0.00 + 5.83 -4.83x + x2 = 0.00 + 5.83 Combine like terms: 0.00 + 5.83 = 5.83 -4.83x + x2 = 5.83 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 = 5.83 + 5.832225 Reorder the terms: 5.832225 + -4.83x + x2 = 5.83 + 5.832225 Combine like terms: 5.83 + 5.832225 = 11.662225 5.832225 + -4.83x + x2 = 11.662225 Factor a perfect square on the left side: (x + -2.415)(x + -2.415) = 11.662225 Calculate the square root of the right side: 3.415 Break this problem into two subproblems by setting (x + -2.415) equal to 3.415 and -3.415.Subproblem 1
x + -2.415 = 3.415 Simplifying x + -2.415 = 3.415 Reorder the terms: -2.415 + x = 3.415 Solving -2.415 + x = 3.415 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 = 3.415 + 2.415 Combine like terms: -2.415 + 2.415 = 0.000 0.000 + x = 3.415 + 2.415 x = 3.415 + 2.415 Combine like terms: 3.415 + 2.415 = 5.83 x = 5.83 Simplifying x = 5.83Subproblem 2
x + -2.415 = -3.415 Simplifying x + -2.415 = -3.415 Reorder the terms: -2.415 + x = -3.415 Solving -2.415 + x = -3.415 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 = -3.415 + 2.415 Combine like terms: -2.415 + 2.415 = 0.000 0.000 + x = -3.415 + 2.415 x = -3.415 + 2.415 Combine like terms: -3.415 + 2.415 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.83, -1}
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