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Simplifying 2x(x + 34) = 268 Reorder the terms: 2x(34 + x) = 268 (34 * 2x + x * 2x) = 268 (68x + 2x2) = 268 Solving 68x + 2x2 = 268 Solving for variable 'x'. Reorder the terms: -268 + 68x + 2x2 = 268 + -268 Combine like terms: 268 + -268 = 0 -268 + 68x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-134 + 34x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-134 + 34x + x2)' equal to zero and attempt to solve: Simplifying -134 + 34x + x2 = 0 Solving -134 + 34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '134' to each side of the equation. -134 + 34x + 134 + x2 = 0 + 134 Reorder the terms: -134 + 134 + 34x + x2 = 0 + 134 Combine like terms: -134 + 134 = 0 0 + 34x + x2 = 0 + 134 34x + x2 = 0 + 134 Combine like terms: 0 + 134 = 134 34x + x2 = 134 The x term is 34x. Take half its coefficient (17). Square it (289) and add it to both sides. Add '289' to each side of the equation. 34x + 289 + x2 = 134 + 289 Reorder the terms: 289 + 34x + x2 = 134 + 289 Combine like terms: 134 + 289 = 423 289 + 34x + x2 = 423 Factor a perfect square on the left side: (x + 17)(x + 17) = 423 Calculate the square root of the right side: 20.566963801 Break this problem into two subproblems by setting (x + 17) equal to 20.566963801 and -20.566963801.Subproblem 1
x + 17 = 20.566963801 Simplifying x + 17 = 20.566963801 Reorder the terms: 17 + x = 20.566963801 Solving 17 + x = 20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 20.566963801 + -17 Combine like terms: 17 + -17 = 0 0 + x = 20.566963801 + -17 x = 20.566963801 + -17 Combine like terms: 20.566963801 + -17 = 3.566963801 x = 3.566963801 Simplifying x = 3.566963801Subproblem 2
x + 17 = -20.566963801 Simplifying x + 17 = -20.566963801 Reorder the terms: 17 + x = -20.566963801 Solving 17 + x = -20.566963801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -20.566963801 + -17 Combine like terms: 17 + -17 = 0 0 + x = -20.566963801 + -17 x = -20.566963801 + -17 Combine like terms: -20.566963801 + -17 = -37.566963801 x = -37.566963801 Simplifying x = -37.566963801Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.566963801, -37.566963801}Solution
x = {3.566963801, -37.566963801}
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