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Simplifying x2 + 5(x + 12) = 162 Reorder the terms: x2 + 5(12 + x) = 162 x2 + (12 * 5 + x * 5) = 162 x2 + (60 + 5x) = 162 Reorder the terms: 60 + 5x + x2 = 162 Solving 60 + 5x + x2 = 162 Solving for variable 'x'. Reorder the terms: 60 + -162 + 5x + x2 = 162 + -162 Combine like terms: 60 + -162 = -102 -102 + 5x + x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -102 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '102' to each side of the equation. -102 + 5x + 102 + x2 = 0 + 102 Reorder the terms: -102 + 102 + 5x + x2 = 0 + 102 Combine like terms: -102 + 102 = 0 0 + 5x + x2 = 0 + 102 5x + x2 = 0 + 102 Combine like terms: 0 + 102 = 102 5x + x2 = 102 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 102 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 102 + 6.25 Combine like terms: 102 + 6.25 = 108.25 6.25 + 5x + x2 = 108.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + 2.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + 2.5 = 10.404326023 Simplifying x + 2.5 = 10.404326023 Reorder the terms: 2.5 + x = 10.404326023 Solving 2.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.404326023 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.404326023 + -2.5 x = 10.404326023 + -2.5 Combine like terms: 10.404326023 + -2.5 = 7.904326023 x = 7.904326023 Simplifying x = 7.904326023Subproblem 2
x + 2.5 = -10.404326023 Simplifying x + 2.5 = -10.404326023 Reorder the terms: 2.5 + x = -10.404326023 Solving 2.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.404326023 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.404326023 + -2.5 x = -10.404326023 + -2.5 Combine like terms: -10.404326023 + -2.5 = -12.904326023 x = -12.904326023 Simplifying x = -12.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.904326023, -12.904326023}
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