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Simplifying x(2 + -3x) = x2 + 7x + -4 (2 * x + -3x * x) = x2 + 7x + -4 (2x + -3x2) = x2 + 7x + -4 Reorder the terms: 2x + -3x2 = -4 + 7x + x2 Solving 2x + -3x2 = -4 + 7x + x2 Solving for variable 'x'. Reorder the terms: 4 + 2x + -7x + -3x2 + -1x2 = -4 + 7x + x2 + 4 + -7x + -1x2 Combine like terms: 2x + -7x = -5x 4 + -5x + -3x2 + -1x2 = -4 + 7x + x2 + 4 + -7x + -1x2 Combine like terms: -3x2 + -1x2 = -4x2 4 + -5x + -4x2 = -4 + 7x + x2 + 4 + -7x + -1x2 Reorder the terms: 4 + -5x + -4x2 = -4 + 4 + 7x + -7x + x2 + -1x2 Combine like terms: -4 + 4 = 0 4 + -5x + -4x2 = 0 + 7x + -7x + x2 + -1x2 4 + -5x + -4x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 4 + -5x + -4x2 = 0 + x2 + -1x2 4 + -5x + -4x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 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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