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Simplifying 2x + 3 = (x + -1)(x + 4) Reorder the terms: 3 + 2x = (x + -1)(x + 4) Reorder the terms: 3 + 2x = (-1 + x)(x + 4) Reorder the terms: 3 + 2x = (-1 + x)(4 + x) Multiply (-1 + x) * (4 + x) 3 + 2x = (-1(4 + x) + x(4 + x)) 3 + 2x = ((4 * -1 + x * -1) + x(4 + x)) 3 + 2x = ((-4 + -1x) + x(4 + x)) 3 + 2x = (-4 + -1x + (4 * x + x * x)) 3 + 2x = (-4 + -1x + (4x + x2)) Combine like terms: -1x + 4x = 3x 3 + 2x = (-4 + 3x + x2) Solving 3 + 2x = -4 + 3x + x2 Solving for variable 'x'. Reorder the terms: 3 + 4 + 2x + -3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2 Combine like terms: 3 + 4 = 7 7 + 2x + -3x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2 Combine like terms: 2x + -3x = -1x 7 + -1x + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2 Reorder the terms: 7 + -1x + -1x2 = -4 + 4 + 3x + -3x + x2 + -1x2 Combine like terms: -4 + 4 = 0 7 + -1x + -1x2 = 0 + 3x + -3x + x2 + -1x2 7 + -1x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 7 + -1x + -1x2 = 0 + x2 + -1x2 7 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -7 + x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x + x2 = 0 + 7 x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 x + x2 = 7 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 7 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 1.25 + x2 = 7.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 0.5 = 2.692582404 Simplifying x + 0.5 = 2.692582404 Reorder the terms: 0.5 + x = 2.692582404 Solving 0.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.692582404 + -0.5 x = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 x = 2.192582404 Simplifying x = 2.192582404Subproblem 2
x + 0.5 = -2.692582404 Simplifying x + 0.5 = -2.692582404 Reorder the terms: 0.5 + x = -2.692582404 Solving 0.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.692582404 + -0.5 x = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 x = -3.192582404 Simplifying x = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.192582404, -3.192582404}
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