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Simplifying 82 = x(x + 4) Reorder the terms: 82 = x(4 + x) 82 = (4 * x + x * x) 82 = (4x + x2) Solving 82 = 4x + x2 Solving for variable 'x'. Reorder the terms: 82 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 82 + -4x + -1x2 = 0 + x2 + -1x2 82 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 82 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -82 + 4x + x2 = 0 Move the constant term to the right: Add '82' to each side of the equation. -82 + 4x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 4x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 4x + x2 = 0 + 82 4x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 4x + x2 = 82 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 = 82 + 4 Reorder the terms: 4 + 4x + x2 = 82 + 4 Combine like terms: 82 + 4 = 86 4 + 4x + x2 = 86 Factor a perfect square on the left side: (x + 2)(x + 2) = 86 Calculate the square root of the right side: 9.273618495 Break this problem into two subproblems by setting (x + 2) equal to 9.273618495 and -9.273618495.Subproblem 1
x + 2 = 9.273618495 Simplifying x + 2 = 9.273618495 Reorder the terms: 2 + x = 9.273618495 Solving 2 + x = 9.273618495 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 = 9.273618495 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.273618495 + -2 x = 9.273618495 + -2 Combine like terms: 9.273618495 + -2 = 7.273618495 x = 7.273618495 Simplifying x = 7.273618495Subproblem 2
x + 2 = -9.273618495 Simplifying x + 2 = -9.273618495 Reorder the terms: 2 + x = -9.273618495 Solving 2 + x = -9.273618495 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 = -9.273618495 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.273618495 + -2 x = -9.273618495 + -2 Combine like terms: -9.273618495 + -2 = -11.273618495 x = -11.273618495 Simplifying x = -11.273618495Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.273618495, -11.273618495}
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