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Simplifying x2 + -4x = x + -3 Reorder the terms: -4x + x2 = x + -3 Reorder the terms: -4x + x2 = -3 + x Solving -4x + x2 = -3 + x Solving for variable 'x'. Reorder the terms: 3 + -4x + -1x + x2 = -3 + x + 3 + -1x Combine like terms: -4x + -1x = -5x 3 + -5x + x2 = -3 + x + 3 + -1x Reorder the terms: 3 + -5x + x2 = -3 + 3 + x + -1x Combine like terms: -3 + 3 = 0 3 + -5x + x2 = 0 + x + -1x 3 + -5x + x2 = x + -1x Combine like terms: x + -1x = 0 3 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x + x2 = 0 + -3 -5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5x + x2 = -3 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5x + x2 = 3.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -2.5 = 1.802775638 Simplifying x + -2.5 = 1.802775638 Reorder the terms: -2.5 + x = 1.802775638 Solving -2.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.802775638 + 2.5 x = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 x = 4.302775638 Simplifying x = 4.302775638Subproblem 2
x + -2.5 = -1.802775638 Simplifying x + -2.5 = -1.802775638 Reorder the terms: -2.5 + x = -1.802775638 Solving -2.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.802775638 + 2.5 x = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 x = 0.697224362 Simplifying x = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.302775638, 0.697224362}
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