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Simplifying 225 = x(14 + x) 225 = (14 * x + x * x) 225 = (14x + x2) Solving 225 = 14x + x2 Solving for variable 'x'. Reorder the terms: 225 + -14x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 225 + -14x + -1x2 = 0 + x2 + -1x2 225 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 225 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -225 + 14x + x2 = 0 Move the constant term to the right: Add '225' to each side of the equation. -225 + 14x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 14x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 14x + x2 = 0 + 225 14x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 14x + x2 = 225 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = 225 + 49 Reorder the terms: 49 + 14x + x2 = 225 + 49 Combine like terms: 225 + 49 = 274 49 + 14x + x2 = 274 Factor a perfect square on the left side: (x + 7)(x + 7) = 274 Calculate the square root of the right side: 16.552945357 Break this problem into two subproblems by setting (x + 7) equal to 16.552945357 and -16.552945357.Subproblem 1
x + 7 = 16.552945357 Simplifying x + 7 = 16.552945357 Reorder the terms: 7 + x = 16.552945357 Solving 7 + x = 16.552945357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 16.552945357 + -7 Combine like terms: 7 + -7 = 0 0 + x = 16.552945357 + -7 x = 16.552945357 + -7 Combine like terms: 16.552945357 + -7 = 9.552945357 x = 9.552945357 Simplifying x = 9.552945357Subproblem 2
x + 7 = -16.552945357 Simplifying x + 7 = -16.552945357 Reorder the terms: 7 + x = -16.552945357 Solving 7 + x = -16.552945357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -16.552945357 + -7 Combine like terms: 7 + -7 = 0 0 + x = -16.552945357 + -7 x = -16.552945357 + -7 Combine like terms: -16.552945357 + -7 = -23.552945357 x = -23.552945357 Simplifying x = -23.552945357Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.552945357, -23.552945357}
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