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Simplifying x + (x + 2) + (x + 4) = x(x + 2) + -33 Reorder the terms: x + (2 + x) + (x + 4) = x(x + 2) + -33 Remove parenthesis around (2 + x) x + 2 + x + (x + 4) = x(x + 2) + -33 Reorder the terms: x + 2 + x + (4 + x) = x(x + 2) + -33 Remove parenthesis around (4 + x) x + 2 + x + 4 + x = x(x + 2) + -33 Reorder the terms: 2 + 4 + x + x + x = x(x + 2) + -33 Combine like terms: 2 + 4 = 6 6 + x + x + x = x(x + 2) + -33 Combine like terms: x + x = 2x 6 + 2x + x = x(x + 2) + -33 Combine like terms: 2x + x = 3x 6 + 3x = x(x + 2) + -33 Reorder the terms: 6 + 3x = x(2 + x) + -33 6 + 3x = (2 * x + x * x) + -33 6 + 3x = (2x + x2) + -33 Reorder the terms: 6 + 3x = -33 + 2x + x2 Solving 6 + 3x = -33 + 2x + x2 Solving for variable 'x'. Reorder the terms: 6 + 33 + 3x + -2x + -1x2 = -33 + 2x + x2 + 33 + -2x + -1x2 Combine like terms: 6 + 33 = 39 39 + 3x + -2x + -1x2 = -33 + 2x + x2 + 33 + -2x + -1x2 Combine like terms: 3x + -2x = 1x 39 + 1x + -1x2 = -33 + 2x + x2 + 33 + -2x + -1x2 Reorder the terms: 39 + 1x + -1x2 = -33 + 33 + 2x + -2x + x2 + -1x2 Combine like terms: -33 + 33 = 0 39 + 1x + -1x2 = 0 + 2x + -2x + x2 + -1x2 39 + 1x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 39 + 1x + -1x2 = 0 + x2 + -1x2 39 + 1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 39 + 1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -39 + -1x + x2 = 0 Move the constant term to the right: Add '39' to each side of the equation. -39 + -1x + 39 + x2 = 0 + 39 Reorder the terms: -39 + 39 + -1x + x2 = 0 + 39 Combine like terms: -39 + 39 = 0 0 + -1x + x2 = 0 + 39 -1x + x2 = 0 + 39 Combine like terms: 0 + 39 = 39 -1x + x2 = 39 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 = 39 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 39 + 0.25 Combine like terms: 39 + 0.25 = 39.25 0.25 + -1x + x2 = 39.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -0.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -0.5 = 6.264982043 Simplifying x + -0.5 = 6.264982043 Reorder the terms: -0.5 + x = 6.264982043 Solving -0.5 + x = 6.264982043 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 = 6.264982043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 6.264982043 + 0.5 x = 6.264982043 + 0.5 Combine like terms: 6.264982043 + 0.5 = 6.764982043 x = 6.764982043 Simplifying x = 6.764982043Subproblem 2
x + -0.5 = -6.264982043 Simplifying x + -0.5 = -6.264982043 Reorder the terms: -0.5 + x = -6.264982043 Solving -0.5 + x = -6.264982043 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 = -6.264982043 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -6.264982043 + 0.5 x = -6.264982043 + 0.5 Combine like terms: -6.264982043 + 0.5 = -5.764982043 x = -5.764982043 Simplifying x = -5.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.764982043, -5.764982043}
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