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Simplifying 34X2 + 34X + 5 = 0 Reorder the terms: 5 + 34X + 34X2 = 0 Solving 5 + 34X + 34X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. 0.1470588235 + X + X2 = 0 Move the constant term to the right: Add '-0.1470588235' to each side of the equation. 0.1470588235 + X + -0.1470588235 + X2 = 0 + -0.1470588235 Reorder the terms: 0.1470588235 + -0.1470588235 + X + X2 = 0 + -0.1470588235 Combine like terms: 0.1470588235 + -0.1470588235 = 0.0000000000 0.0000000000 + X + X2 = 0 + -0.1470588235 X + X2 = 0 + -0.1470588235 Combine like terms: 0 + -0.1470588235 = -0.1470588235 X + X2 = -0.1470588235 The X term is X. 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. + 0.25 + X2 = -0.1470588235 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + X2 = -0.1470588235 + 0.25 Combine like terms: -0.1470588235 + 0.25 = 0.1029411765 1.25 + X2 = 0.1029411765 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 0.1029411765 Calculate the square root of the right side: 0.320844474 Break this problem into two subproblems by setting (X + 0.5) equal to 0.320844474 and -0.320844474.Subproblem 1
X + 0.5 = 0.320844474 Simplifying X + 0.5 = 0.320844474 Reorder the terms: 0.5 + X = 0.320844474 Solving 0.5 + X = 0.320844474 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 = 0.320844474 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 0.320844474 + -0.5 X = 0.320844474 + -0.5 Combine like terms: 0.320844474 + -0.5 = -0.179155526 X = -0.179155526 Simplifying X = -0.179155526Subproblem 2
X + 0.5 = -0.320844474 Simplifying X + 0.5 = -0.320844474 Reorder the terms: 0.5 + X = -0.320844474 Solving 0.5 + X = -0.320844474 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 = -0.320844474 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -0.320844474 + -0.5 X = -0.320844474 + -0.5 Combine like terms: -0.320844474 + -0.5 = -0.820844474 X = -0.820844474 Simplifying X = -0.820844474Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.179155526, -0.820844474}
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