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Simplifying (x + -2)(x + 1) = 13 Reorder the terms: (-2 + x)(x + 1) = 13 Reorder the terms: (-2 + x)(1 + x) = 13 Multiply (-2 + x) * (1 + x) (-2(1 + x) + x(1 + x)) = 13 ((1 * -2 + x * -2) + x(1 + x)) = 13 ((-2 + -2x) + x(1 + x)) = 13 (-2 + -2x + (1 * x + x * x)) = 13 (-2 + -2x + (1x + x2)) = 13 Combine like terms: -2x + 1x = -1x (-2 + -1x + x2) = 13 Solving -2 + -1x + x2 = 13 Solving for variable 'x'. Reorder the terms: -2 + -13 + -1x + x2 = 13 + -13 Combine like terms: -2 + -13 = -15 -15 + -1x + x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -15 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -1x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -1x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x + x2 = 0 + 15 -1x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1x + x2 = 15 The x term is -1x. 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. -1x + 0.25 + x2 = 15 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 15 + 0.25 Combine like terms: 15 + 0.25 = 15.25 0.25 + -1x + x2 = 15.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (x + -0.5) equal to 3.905124838 and -3.905124838.Subproblem 1
x + -0.5 = 3.905124838 Simplifying x + -0.5 = 3.905124838 Reorder the terms: -0.5 + x = 3.905124838 Solving -0.5 + x = 3.905124838 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 = 3.905124838 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.905124838 + 0.5 x = 3.905124838 + 0.5 Combine like terms: 3.905124838 + 0.5 = 4.405124838 x = 4.405124838 Simplifying x = 4.405124838Subproblem 2
x + -0.5 = -3.905124838 Simplifying x + -0.5 = -3.905124838 Reorder the terms: -0.5 + x = -3.905124838 Solving -0.5 + x = -3.905124838 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 = -3.905124838 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.905124838 + 0.5 x = -3.905124838 + 0.5 Combine like terms: -3.905124838 + 0.5 = -3.405124838 x = -3.405124838 Simplifying x = -3.405124838Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.405124838, -3.405124838}
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