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Simplifying 2(x2 + -34x + -136) = 0 Reorder the terms: 2(-136 + -34x + x2) = 0 (-136 * 2 + -34x * 2 + x2 * 2) = 0 (-272 + -68x + 2x2) = 0 Solving -272 + -68x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-136 + -34x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-136 + -34x + x2)' equal to zero and attempt to solve: Simplifying -136 + -34x + x2 = 0 Solving -136 + -34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + -34x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + -34x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + -34x + x2 = 0 + 136 -34x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 -34x + x2 = 136 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 = 136 + 289 Reorder the terms: 289 + -34x + x2 = 136 + 289 Combine like terms: 136 + 289 = 425 289 + -34x + x2 = 425 Factor a perfect square on the left side: (x + -17)(x + -17) = 425 Calculate the square root of the right side: 20.615528128 Break this problem into two subproblems by setting (x + -17) equal to 20.615528128 and -20.615528128.Subproblem 1
x + -17 = 20.615528128 Simplifying x + -17 = 20.615528128 Reorder the terms: -17 + x = 20.615528128 Solving -17 + x = 20.615528128 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 = 20.615528128 + 17 Combine like terms: -17 + 17 = 0 0 + x = 20.615528128 + 17 x = 20.615528128 + 17 Combine like terms: 20.615528128 + 17 = 37.615528128 x = 37.615528128 Simplifying x = 37.615528128Subproblem 2
x + -17 = -20.615528128 Simplifying x + -17 = -20.615528128 Reorder the terms: -17 + x = -20.615528128 Solving -17 + x = -20.615528128 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 = -20.615528128 + 17 Combine like terms: -17 + 17 = 0 0 + x = -20.615528128 + 17 x = -20.615528128 + 17 Combine like terms: -20.615528128 + 17 = -3.615528128 x = -3.615528128 Simplifying x = -3.615528128Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.615528128, -3.615528128}Solution
x = {37.615528128, -3.615528128}
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