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Simplifying 4x2 + -1 = 5x + 3 Reorder the terms: -1 + 4x2 = 5x + 3 Reorder the terms: -1 + 4x2 = 3 + 5x Solving -1 + 4x2 = 3 + 5x Solving for variable 'x'. Reorder the terms: -1 + -3 + -5x + 4x2 = 3 + 5x + -3 + -5x Combine like terms: -1 + -3 = -4 -4 + -5x + 4x2 = 3 + 5x + -3 + -5x Reorder the terms: -4 + -5x + 4x2 = 3 + -3 + 5x + -5x Combine like terms: 3 + -3 = 0 -4 + -5x + 4x2 = 0 + 5x + -5x -4 + -5x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 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 = 1.804247642 x = 1.804247642 Simplifying x = 1.804247642Subproblem 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 = -0.554247642 x = -0.554247642 Simplifying x = -0.554247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.804247642, -0.554247642}
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