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Simplifying 3x + 2 + 5(x + -1) * 8x = 17 Reorder the terms: 3x + 2 + 5(-1 + x) * 8x = 17 Reorder the terms for easier multiplication: 3x + 2 + 5 * 8x(-1 + x) = 17 Multiply 5 * 8 3x + 2 + 40x(-1 + x) = 17 3x + 2 + (-1 * 40x + x * 40x) = 17 3x + 2 + (-40x + 40x2) = 17 Reorder the terms: 2 + 3x + -40x + 40x2 = 17 Combine like terms: 3x + -40x = -37x 2 + -37x + 40x2 = 17 Solving 2 + -37x + 40x2 = 17 Solving for variable 'x'. Reorder the terms: 2 + -17 + -37x + 40x2 = 17 + -17 Combine like terms: 2 + -17 = -15 -15 + -37x + 40x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -15 + -37x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.375 + -0.925x + x2 = 0.0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.925x + 0.375 + x2 = 0.0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.925x + x2 = 0.0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.925x + x2 = 0.0 + 0.375 -0.925x + x2 = 0.0 + 0.375 Combine like terms: 0.0 + 0.375 = 0.375 -0.925x + x2 = 0.375 The x term is -0.925x. Take half its coefficient (-0.4625). Square it (0.21390625) and add it to both sides. Add '0.21390625' to each side of the equation. -0.925x + 0.21390625 + x2 = 0.375 + 0.21390625 Reorder the terms: 0.21390625 + -0.925x + x2 = 0.375 + 0.21390625 Combine like terms: 0.375 + 0.21390625 = 0.58890625 0.21390625 + -0.925x + x2 = 0.58890625 Factor a perfect square on the left side: (x + -0.4625)(x + -0.4625) = 0.58890625 Calculate the square root of the right side: 0.767402274 Break this problem into two subproblems by setting (x + -0.4625) equal to 0.767402274 and -0.767402274.Subproblem 1
x + -0.4625 = 0.767402274 Simplifying x + -0.4625 = 0.767402274 Reorder the terms: -0.4625 + x = 0.767402274 Solving -0.4625 + x = 0.767402274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4625' to each side of the equation. -0.4625 + 0.4625 + x = 0.767402274 + 0.4625 Combine like terms: -0.4625 + 0.4625 = 0.0000 0.0000 + x = 0.767402274 + 0.4625 x = 0.767402274 + 0.4625 Combine like terms: 0.767402274 + 0.4625 = 1.229902274 x = 1.229902274 Simplifying x = 1.229902274Subproblem 2
x + -0.4625 = -0.767402274 Simplifying x + -0.4625 = -0.767402274 Reorder the terms: -0.4625 + x = -0.767402274 Solving -0.4625 + x = -0.767402274 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4625' to each side of the equation. -0.4625 + 0.4625 + x = -0.767402274 + 0.4625 Combine like terms: -0.4625 + 0.4625 = 0.0000 0.0000 + x = -0.767402274 + 0.4625 x = -0.767402274 + 0.4625 Combine like terms: -0.767402274 + 0.4625 = -0.304902274 x = -0.304902274 Simplifying x = -0.304902274Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.229902274, -0.304902274}
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