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Simplifying 4x2 + 2x = 4 + -3x Reorder the terms: 2x + 4x2 = 4 + -3x Solving 2x + 4x2 = 4 + -3x Solving for variable 'x'. Reorder the terms: -4 + 2x + 3x + 4x2 = 4 + -3x + -4 + 3x Combine like terms: 2x + 3x = 5x -4 + 5x + 4x2 = 4 + -3x + -4 + 3x Reorder the terms: -4 + 5x + 4x2 = 4 + -4 + -3x + 3x Combine like terms: 4 + -4 = 0 -4 + 5x + 4x2 = 0 + -3x + 3x -4 + 5x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -4 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 1.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.25x + x2 = 0 + 1 1.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.25x + x2 = 1 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 1 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 1 + 0.390625 Combine like terms: 1 + 0.390625 = 1.390625 0.390625 + 1.25x + x2 = 1.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + 0.625) equal to 1.179247642 and -1.179247642.Subproblem 1
x + 0.625 = 1.179247642 Simplifying x + 0.625 = 1.179247642 Reorder the terms: 0.625 + x = 1.179247642 Solving 0.625 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.179247642 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.179247642 + -0.625 x = 1.179247642 + -0.625 Combine like terms: 1.179247642 + -0.625 = 0.554247642 x = 0.554247642 Simplifying x = 0.554247642Subproblem 2
x + 0.625 = -1.179247642 Simplifying x + 0.625 = -1.179247642 Reorder the terms: 0.625 + x = -1.179247642 Solving 0.625 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.179247642 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.179247642 + -0.625 x = -1.179247642 + -0.625 Combine like terms: -1.179247642 + -0.625 = -1.804247642 x = -1.804247642 Simplifying x = -1.804247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.554247642, -1.804247642}
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