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Simplifying 24 * 14 = x(x + 8) Multiply 24 * 14 336 = x(x + 8) Reorder the terms: 336 = x(8 + x) 336 = (8 * x + x * x) 336 = (8x + x2) Solving 336 = 8x + x2 Solving for variable 'x'. Reorder the terms: 336 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 336 + -8x + -1x2 = 0 + x2 + -1x2 336 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 336 + -8x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -336 + 8x + x2 = 0 Move the constant term to the right: Add '336' to each side of the equation. -336 + 8x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + 8x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + 8x + x2 = 0 + 336 8x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 8x + x2 = 336 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 336 + 16 Reorder the terms: 16 + 8x + x2 = 336 + 16 Combine like terms: 336 + 16 = 352 16 + 8x + x2 = 352 Factor a perfect square on the left side: (x + 4)(x + 4) = 352 Calculate the square root of the right side: 18.761663039 Break this problem into two subproblems by setting (x + 4) equal to 18.761663039 and -18.761663039.Subproblem 1
x + 4 = 18.761663039 Simplifying x + 4 = 18.761663039 Reorder the terms: 4 + x = 18.761663039 Solving 4 + x = 18.761663039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 18.761663039 + -4 Combine like terms: 4 + -4 = 0 0 + x = 18.761663039 + -4 x = 18.761663039 + -4 Combine like terms: 18.761663039 + -4 = 14.761663039 x = 14.761663039 Simplifying x = 14.761663039Subproblem 2
x + 4 = -18.761663039 Simplifying x + 4 = -18.761663039 Reorder the terms: 4 + x = -18.761663039 Solving 4 + x = -18.761663039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -18.761663039 + -4 Combine like terms: 4 + -4 = 0 0 + x = -18.761663039 + -4 x = -18.761663039 + -4 Combine like terms: -18.761663039 + -4 = -22.761663039 x = -22.761663039 Simplifying x = -22.761663039Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.761663039, -22.761663039}
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