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Simplifying 3x + -2 = -4x2 + 16x Reorder the terms: -2 + 3x = -4x2 + 16x Reorder the terms: -2 + 3x = 16x + -4x2 Solving -2 + 3x = 16x + -4x2 Solving for variable 'x'. Combine like terms: 3x + -16x = -13x -2 + -13x + 4x2 = 16x + -4x2 + -16x + 4x2 Reorder the terms: -2 + -13x + 4x2 = 16x + -16x + -4x2 + 4x2 Combine like terms: 16x + -16x = 0 -2 + -13x + 4x2 = 0 + -4x2 + 4x2 -2 + -13x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -2 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -3.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.25x + x2 = 0 + 0.5 -3.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.25x + x2 = 0.5 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 0.5 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 0.5 + 2.640625 Combine like terms: 0.5 + 2.640625 = 3.140625 2.640625 + -3.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -1.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -1.625 = 1.77218086 Simplifying x + -1.625 = 1.77218086 Reorder the terms: -1.625 + x = 1.77218086 Solving -1.625 + x = 1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.77218086 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.77218086 + 1.625 x = 1.77218086 + 1.625 Combine like terms: 1.77218086 + 1.625 = 3.39718086 x = 3.39718086 Simplifying x = 3.39718086Subproblem 2
x + -1.625 = -1.77218086 Simplifying x + -1.625 = -1.77218086 Reorder the terms: -1.625 + x = -1.77218086 Solving -1.625 + x = -1.77218086 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.77218086 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.77218086 + 1.625 x = -1.77218086 + 1.625 Combine like terms: -1.77218086 + 1.625 = -0.14718086 x = -0.14718086 Simplifying x = -0.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.39718086, -0.14718086}
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