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Simplifying (x + -1)(x + -1) = 3x + 5 Reorder the terms: (-1 + x)(x + -1) = 3x + 5 Reorder the terms: (-1 + x)(-1 + x) = 3x + 5 Multiply (-1 + x) * (-1 + x) (-1(-1 + x) + x(-1 + x)) = 3x + 5 ((-1 * -1 + x * -1) + x(-1 + x)) = 3x + 5 ((1 + -1x) + x(-1 + x)) = 3x + 5 (1 + -1x + (-1 * x + x * x)) = 3x + 5 (1 + -1x + (-1x + x2)) = 3x + 5 Combine like terms: -1x + -1x = -2x (1 + -2x + x2) = 3x + 5 Reorder the terms: 1 + -2x + x2 = 5 + 3x Solving 1 + -2x + x2 = 5 + 3x Solving for variable 'x'. Reorder the terms: 1 + -5 + -2x + -3x + x2 = 5 + 3x + -5 + -3x Combine like terms: 1 + -5 = -4 -4 + -2x + -3x + x2 = 5 + 3x + -5 + -3x Combine like terms: -2x + -3x = -5x -4 + -5x + x2 = 5 + 3x + -5 + -3x Reorder the terms: -4 + -5x + x2 = 5 + -5 + 3x + -3x Combine like terms: 5 + -5 = 0 -4 + -5x + x2 = 0 + 3x + -3x -4 + -5x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -4 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x + x2 = 0 + 4 -5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5x + x2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5x + x2 = 10.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -2.5 = 3.201562119 Simplifying x + -2.5 = 3.201562119 Reorder the terms: -2.5 + x = 3.201562119 Solving -2.5 + x = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.201562119 + 2.5 x = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x = 5.701562119 Simplifying x = 5.701562119Subproblem 2
x + -2.5 = -3.201562119 Simplifying x + -2.5 = -3.201562119 Reorder the terms: -2.5 + x = -3.201562119 Solving -2.5 + x = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.201562119 + 2.5 x = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x = -0.701562119 Simplifying x = -0.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.701562119, -0.701562119}
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