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Simplifying 2x2 + -5 + 2 = (x + -3)(x + -2) + 3x Reorder the terms: -5 + 2 + 2x2 = (x + -3)(x + -2) + 3x Combine like terms: -5 + 2 = -3 -3 + 2x2 = (x + -3)(x + -2) + 3x Reorder the terms: -3 + 2x2 = (-3 + x)(x + -2) + 3x Reorder the terms: -3 + 2x2 = (-3 + x)(-2 + x) + 3x Multiply (-3 + x) * (-2 + x) -3 + 2x2 = (-3(-2 + x) + x(-2 + x)) + 3x -3 + 2x2 = ((-2 * -3 + x * -3) + x(-2 + x)) + 3x -3 + 2x2 = ((6 + -3x) + x(-2 + x)) + 3x -3 + 2x2 = (6 + -3x + (-2 * x + x * x)) + 3x -3 + 2x2 = (6 + -3x + (-2x + x2)) + 3x Combine like terms: -3x + -2x = -5x -3 + 2x2 = (6 + -5x + x2) + 3x Reorder the terms: -3 + 2x2 = 6 + -5x + 3x + x2 Combine like terms: -5x + 3x = -2x -3 + 2x2 = 6 + -2x + x2 Solving -3 + 2x2 = 6 + -2x + x2 Solving for variable 'x'. Reorder the terms: -3 + -6 + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: -3 + -6 = -9 -9 + 2x + 2x2 + -1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -9 + 2x + 1x2 = 6 + -2x + x2 + -6 + 2x + -1x2 Reorder the terms: -9 + 2x + 1x2 = 6 + -6 + -2x + 2x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -9 + 2x + 1x2 = 0 + -2x + 2x + x2 + -1x2 -9 + 2x + 1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -9 + 2x + 1x2 = 0 + x2 + -1x2 -9 + 2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + 2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2x + x2 = 0 + 9 2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 2x + x2 = 9 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 9 + 1 Reorder the terms: 1 + 2x + x2 = 9 + 1 Combine like terms: 9 + 1 = 10 1 + 2x + x2 = 10 Factor a perfect square on the left side: (x + 1)(x + 1) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + 1) equal to 3.16227766 and -3.16227766.Subproblem 1
x + 1 = 3.16227766 Simplifying x + 1 = 3.16227766 Reorder the terms: 1 + x = 3.16227766 Solving 1 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.16227766 + -1 x = 3.16227766 + -1 Combine like terms: 3.16227766 + -1 = 2.16227766 x = 2.16227766 Simplifying x = 2.16227766Subproblem 2
x + 1 = -3.16227766 Simplifying x + 1 = -3.16227766 Reorder the terms: 1 + x = -3.16227766 Solving 1 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.16227766 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.16227766 + -1 x = -3.16227766 + -1 Combine like terms: -3.16227766 + -1 = -4.16227766 x = -4.16227766 Simplifying x = -4.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.16227766, -4.16227766}
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