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Simplifying (7 + 17) * 7 = (x + 14) * x Combine like terms: 7 + 17 = 24 (24) * 7 = (x + 14) * x Multiply 24 * 7 168 = (x + 14) * x Reorder the terms: 168 = (14 + x) * x Reorder the terms for easier multiplication: 168 = x(14 + x) 168 = (14 * x + x * x) 168 = (14x + x2) Solving 168 = 14x + x2 Solving for variable 'x'. Reorder the terms: 168 + -14x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 168 + -14x + -1x2 = 0 + x2 + -1x2 168 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 168 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -168 + 14x + x2 = 0 Move the constant term to the right: Add '168' to each side of the equation. -168 + 14x + 168 + x2 = 0 + 168 Reorder the terms: -168 + 168 + 14x + x2 = 0 + 168 Combine like terms: -168 + 168 = 0 0 + 14x + x2 = 0 + 168 14x + x2 = 0 + 168 Combine like terms: 0 + 168 = 168 14x + x2 = 168 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 = 168 + 49 Reorder the terms: 49 + 14x + x2 = 168 + 49 Combine like terms: 168 + 49 = 217 49 + 14x + x2 = 217 Factor a perfect square on the left side: (x + 7)(x + 7) = 217 Calculate the square root of the right side: 14.730919863 Break this problem into two subproblems by setting (x + 7) equal to 14.730919863 and -14.730919863.Subproblem 1
x + 7 = 14.730919863 Simplifying x + 7 = 14.730919863 Reorder the terms: 7 + x = 14.730919863 Solving 7 + x = 14.730919863 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 = 14.730919863 + -7 Combine like terms: 7 + -7 = 0 0 + x = 14.730919863 + -7 x = 14.730919863 + -7 Combine like terms: 14.730919863 + -7 = 7.730919863 x = 7.730919863 Simplifying x = 7.730919863Subproblem 2
x + 7 = -14.730919863 Simplifying x + 7 = -14.730919863 Reorder the terms: 7 + x = -14.730919863 Solving 7 + x = -14.730919863 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 = -14.730919863 + -7 Combine like terms: 7 + -7 = 0 0 + x = -14.730919863 + -7 x = -14.730919863 + -7 Combine like terms: -14.730919863 + -7 = -21.730919863 x = -21.730919863 Simplifying x = -21.730919863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.730919863, -21.730919863}
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