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Simplifying 2x2 + -5x + -2 = (x + -3)(x + -2) + 3x Reorder the terms: -2 + -5x + 2x2 = (x + -3)(x + -2) + 3x Reorder the terms: -2 + -5x + 2x2 = (-3 + x)(x + -2) + 3x Reorder the terms: -2 + -5x + 2x2 = (-3 + x)(-2 + x) + 3x Multiply (-3 + x) * (-2 + x) -2 + -5x + 2x2 = (-3(-2 + x) + x(-2 + x)) + 3x -2 + -5x + 2x2 = ((-2 * -3 + x * -3) + x(-2 + x)) + 3x -2 + -5x + 2x2 = ((6 + -3x) + x(-2 + x)) + 3x -2 + -5x + 2x2 = (6 + -3x + (-2 * x + x * x)) + 3x -2 + -5x + 2x2 = (6 + -3x + (-2x + x2)) + 3x Combine like terms: -3x + -2x = -5x -2 + -5x + 2x2 = (6 + -5x + x2) + 3x Reorder the terms: -2 + -5x + 2x2 = 6 + -5x + 3x + x2 Combine like terms: -5x + 3x = -2x -2 + -5x + 2x2 = 6 + -2x + x2 Solving -2 + -5x + 2x2 = 6 + -2x + x2 Solving for variable 'x'. Reorder the terms: -2 + -6 + -5x + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: -2 + -6 = -8 -8 + -5x + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: -5x + 2x = -3x -8 + -3x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -8 + -3x + 1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Reorder the terms: -8 + -3x + 1x2 = 6 + -6 + -2x + 2x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -8 + -3x + 1x2 = 0 + -2x + 2x + x2 + -1x2 -8 + -3x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -8 + -3x + 1x2 = 0 + x2 + -1x2 -8 + -3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -3x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -3x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x + x2 = 0 + 8 -3x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3x + x2 = 8 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3x + x2 = 10.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -1.5 = 3.201562119 Simplifying x + -1.5 = 3.201562119 Reorder the terms: -1.5 + x = 3.201562119 Solving -1.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.201562119 + 1.5 x = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 x = 4.701562119 Simplifying x = 4.701562119Subproblem 2
x + -1.5 = -3.201562119 Simplifying x + -1.5 = -3.201562119 Reorder the terms: -1.5 + x = -3.201562119 Solving -1.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.201562119 + 1.5 x = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 x = -1.701562119 Simplifying x = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.701562119, -1.701562119}
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