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Simplifying 17x2 = 17x + 7 Reorder the terms: 17x2 = 7 + 17x Solving 17x2 = 7 + 17x Solving for variable 'x'. Reorder the terms: -7 + -17x + 17x2 = 7 + 17x + -7 + -17x Reorder the terms: -7 + -17x + 17x2 = 7 + -7 + 17x + -17x Combine like terms: 7 + -7 = 0 -7 + -17x + 17x2 = 0 + 17x + -17x -7 + -17x + 17x2 = 17x + -17x Combine like terms: 17x + -17x = 0 -7 + -17x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.4117647059 + -1x + x2 = 0 Move the constant term to the right: Add '0.4117647059' to each side of the equation. -0.4117647059 + -1x + 0.4117647059 + x2 = 0 + 0.4117647059 Reorder the terms: -0.4117647059 + 0.4117647059 + -1x + x2 = 0 + 0.4117647059 Combine like terms: -0.4117647059 + 0.4117647059 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.4117647059 -1x + x2 = 0 + 0.4117647059 Combine like terms: 0 + 0.4117647059 = 0.4117647059 -1x + x2 = 0.4117647059 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.4117647059 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.4117647059 + 0.25 Combine like terms: 0.4117647059 + 0.25 = 0.6617647059 0.25 + -1x + x2 = 0.6617647059 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.6617647059 Calculate the square root of the right side: 0.813489217 Break this problem into two subproblems by setting (x + -0.5) equal to 0.813489217 and -0.813489217.Subproblem 1
x + -0.5 = 0.813489217 Simplifying x + -0.5 = 0.813489217 Reorder the terms: -0.5 + x = 0.813489217 Solving -0.5 + x = 0.813489217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.813489217 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.813489217 + 0.5 x = 0.813489217 + 0.5 Combine like terms: 0.813489217 + 0.5 = 1.313489217 x = 1.313489217 Simplifying x = 1.313489217Subproblem 2
x + -0.5 = -0.813489217 Simplifying x + -0.5 = -0.813489217 Reorder the terms: -0.5 + x = -0.813489217 Solving -0.5 + x = -0.813489217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.813489217 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.813489217 + 0.5 x = -0.813489217 + 0.5 Combine like terms: -0.813489217 + 0.5 = -0.313489217 x = -0.313489217 Simplifying x = -0.313489217Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.313489217, -0.313489217}
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