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Simplifying 169 = 25 + x2 + 4x + -4 Reorder the terms: 169 = 25 + -4 + 4x + x2 Combine like terms: 25 + -4 = 21 169 = 21 + 4x + x2 Solving 169 = 21 + 4x + x2 Solving for variable 'x'. Combine like terms: 169 + -21 = 148 148 + -4x + -1x2 = 21 + 4x + x2 + -21 + -4x + -1x2 Reorder the terms: 148 + -4x + -1x2 = 21 + -21 + 4x + -4x + x2 + -1x2 Combine like terms: 21 + -21 = 0 148 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2 148 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 148 + -4x + -1x2 = 0 + x2 + -1x2 148 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 148 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -148 + 4x + x2 = 0 Move the constant term to the right: Add '148' to each side of the equation. -148 + 4x + 148 + x2 = 0 + 148 Reorder the terms: -148 + 148 + 4x + x2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + 4x + x2 = 0 + 148 4x + x2 = 0 + 148 Combine like terms: 0 + 148 = 148 4x + x2 = 148 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 = 148 + 4 Reorder the terms: 4 + 4x + x2 = 148 + 4 Combine like terms: 148 + 4 = 152 4 + 4x + x2 = 152 Factor a perfect square on the left side: (x + 2)(x + 2) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (x + 2) equal to 12.328828006 and -12.328828006.Subproblem 1
x + 2 = 12.328828006 Simplifying x + 2 = 12.328828006 Reorder the terms: 2 + x = 12.328828006 Solving 2 + x = 12.328828006 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 = 12.328828006 + -2 Combine like terms: 2 + -2 = 0 0 + x = 12.328828006 + -2 x = 12.328828006 + -2 Combine like terms: 12.328828006 + -2 = 10.328828006 x = 10.328828006 Simplifying x = 10.328828006Subproblem 2
x + 2 = -12.328828006 Simplifying x + 2 = -12.328828006 Reorder the terms: 2 + x = -12.328828006 Solving 2 + x = -12.328828006 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 = -12.328828006 + -2 Combine like terms: 2 + -2 = 0 0 + x = -12.328828006 + -2 x = -12.328828006 + -2 Combine like terms: -12.328828006 + -2 = -14.328828006 x = -14.328828006 Simplifying x = -14.328828006Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.328828006, -14.328828006}
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