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Simplifying x2 + 3x + -5 = 4x + -2 Reorder the terms: -5 + 3x + x2 = 4x + -2 Reorder the terms: -5 + 3x + x2 = -2 + 4x Solving -5 + 3x + x2 = -2 + 4x Solving for variable 'x'. Reorder the terms: -5 + 2 + 3x + -4x + x2 = -2 + 4x + 2 + -4x Combine like terms: -5 + 2 = -3 -3 + 3x + -4x + x2 = -2 + 4x + 2 + -4x Combine like terms: 3x + -4x = -1x -3 + -1x + x2 = -2 + 4x + 2 + -4x Reorder the terms: -3 + -1x + x2 = -2 + 2 + 4x + -4x Combine like terms: -2 + 2 = 0 -3 + -1x + x2 = 0 + 4x + -4x -3 + -1x + x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -3 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -1x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -1x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x + x2 = 0 + 3 -1x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1x + x2 = 3 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 3 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1x + x2 = 3.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -0.5 = 1.802775638 Simplifying x + -0.5 = 1.802775638 Reorder the terms: -0.5 + x = 1.802775638 Solving -0.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.802775638 + 0.5 x = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 x = 2.302775638 Simplifying x = 2.302775638Subproblem 2
x + -0.5 = -1.802775638 Simplifying x + -0.5 = -1.802775638 Reorder the terms: -0.5 + x = -1.802775638 Solving -0.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.802775638 + 0.5 x = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 x = -1.302775638 Simplifying x = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.302775638, -1.302775638}
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