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Simplifying 2(x + -1) + 3 = (x + -3)(x + 1) Reorder the terms: 2(-1 + x) + 3 = (x + -3)(x + 1) (-1 * 2 + x * 2) + 3 = (x + -3)(x + 1) (-2 + 2x) + 3 = (x + -3)(x + 1) Reorder the terms: -2 + 3 + 2x = (x + -3)(x + 1) Combine like terms: -2 + 3 = 1 1 + 2x = (x + -3)(x + 1) Reorder the terms: 1 + 2x = (-3 + x)(x + 1) Reorder the terms: 1 + 2x = (-3 + x)(1 + x) Multiply (-3 + x) * (1 + x) 1 + 2x = (-3(1 + x) + x(1 + x)) 1 + 2x = ((1 * -3 + x * -3) + x(1 + x)) 1 + 2x = ((-3 + -3x) + x(1 + x)) 1 + 2x = (-3 + -3x + (1 * x + x * x)) 1 + 2x = (-3 + -3x + (1x + x2)) Combine like terms: -3x + 1x = -2x 1 + 2x = (-3 + -2x + x2) Solving 1 + 2x = -3 + -2x + x2 Solving for variable 'x'. Reorder the terms: 1 + 3 + 2x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 1 + 3 = 4 4 + 2x + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Combine like terms: 2x + 2x = 4x 4 + 4x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2 Reorder the terms: 4 + 4x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2 Combine like terms: -3 + 3 = 0 4 + 4x + -1x2 = 0 + -2x + 2x + x2 + -1x2 4 + 4x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 4 + 4x + -1x2 = 0 + x2 + -1x2 4 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + -4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4x + x2 = 0 + 4 -4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4x + x2 = 4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4 + 4 Reorder the terms: 4 + -4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4x + x2 = 8 Factor a perfect square on the left side: (x + -2)(x + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -2 = 2.828427125 Simplifying x + -2 = 2.828427125 Reorder the terms: -2 + x = 2.828427125 Solving -2 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.828427125 + 2 x = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x = 4.828427125 Simplifying x = 4.828427125Subproblem 2
x + -2 = -2.828427125 Simplifying x + -2 = -2.828427125 Reorder the terms: -2 + x = -2.828427125 Solving -2 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.828427125 + 2 x = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x = -0.828427125 Simplifying x = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.828427125, -0.828427125}
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