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Simplifying 84 = (x + 7) * x + 2 Reorder the terms: 84 = (7 + x) * x + 2 Reorder the terms for easier multiplication: 84 = x(7 + x) + 2 84 = (7 * x + x * x) + 2 84 = (7x + x2) + 2 Reorder the terms: 84 = 2 + 7x + x2 Solving 84 = 2 + 7x + x2 Solving for variable 'x'. Combine like terms: 84 + -2 = 82 82 + -7x + -1x2 = 2 + 7x + x2 + -2 + -7x + -1x2 Reorder the terms: 82 + -7x + -1x2 = 2 + -2 + 7x + -7x + x2 + -1x2 Combine like terms: 2 + -2 = 0 82 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2 82 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 82 + -7x + -1x2 = 0 + x2 + -1x2 82 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 82 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -82 + 7x + x2 = 0 Move the constant term to the right: Add '82' to each side of the equation. -82 + 7x + 82 + x2 = 0 + 82 Reorder the terms: -82 + 82 + 7x + x2 = 0 + 82 Combine like terms: -82 + 82 = 0 0 + 7x + x2 = 0 + 82 7x + x2 = 0 + 82 Combine like terms: 0 + 82 = 82 7x + x2 = 82 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 82 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 82 + 12.25 Combine like terms: 82 + 12.25 = 94.25 12.25 + 7x + x2 = 94.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 94.25 Calculate the square root of the right side: 9.708243919 Break this problem into two subproblems by setting (x + 3.5) equal to 9.708243919 and -9.708243919.Subproblem 1
x + 3.5 = 9.708243919 Simplifying x + 3.5 = 9.708243919 Reorder the terms: 3.5 + x = 9.708243919 Solving 3.5 + x = 9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 9.708243919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 9.708243919 + -3.5 x = 9.708243919 + -3.5 Combine like terms: 9.708243919 + -3.5 = 6.208243919 x = 6.208243919 Simplifying x = 6.208243919Subproblem 2
x + 3.5 = -9.708243919 Simplifying x + 3.5 = -9.708243919 Reorder the terms: 3.5 + x = -9.708243919 Solving 3.5 + x = -9.708243919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -9.708243919 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -9.708243919 + -3.5 x = -9.708243919 + -3.5 Combine like terms: -9.708243919 + -3.5 = -13.208243919 x = -13.208243919 Simplifying x = -13.208243919Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.208243919, -13.208243919}
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