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Simplifying 169 = x2 + 7x Reorder the terms: 169 = 7x + x2 Solving 169 = 7x + x2 Solving for variable 'x'. Reorder the terms: 169 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 169 + -7x + -1x2 = 0 + x2 + -1x2 169 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 169 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -169 + 7x + x2 = 0 Move the constant term to the right: Add '169' to each side of the equation. -169 + 7x + 169 + x2 = 0 + 169 Reorder the terms: -169 + 169 + 7x + x2 = 0 + 169 Combine like terms: -169 + 169 = 0 0 + 7x + x2 = 0 + 169 7x + x2 = 0 + 169 Combine like terms: 0 + 169 = 169 7x + x2 = 169 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 = 169 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 169 + 12.25 Combine like terms: 169 + 12.25 = 181.25 12.25 + 7x + x2 = 181.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 181.25 Calculate the square root of the right side: 13.462912018 Break this problem into two subproblems by setting (x + 3.5) equal to 13.462912018 and -13.462912018.Subproblem 1
x + 3.5 = 13.462912018 Simplifying x + 3.5 = 13.462912018 Reorder the terms: 3.5 + x = 13.462912018 Solving 3.5 + x = 13.462912018 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 = 13.462912018 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 13.462912018 + -3.5 x = 13.462912018 + -3.5 Combine like terms: 13.462912018 + -3.5 = 9.962912018 x = 9.962912018 Simplifying x = 9.962912018Subproblem 2
x + 3.5 = -13.462912018 Simplifying x + 3.5 = -13.462912018 Reorder the terms: 3.5 + x = -13.462912018 Solving 3.5 + x = -13.462912018 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 = -13.462912018 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -13.462912018 + -3.5 x = -13.462912018 + -3.5 Combine like terms: -13.462912018 + -3.5 = -16.962912018 x = -16.962912018 Simplifying x = -16.962912018Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.962912018, -16.962912018}
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