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Simplifying 29x2 + -30x + 5 = 0 Reorder the terms: 5 + -30x + 29x2 = 0 Solving 5 + -30x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. 0.1724137931 + -1.034482759x + x2 = 0 Move the constant term to the right: Add '-0.1724137931' to each side of the equation. 0.1724137931 + -1.034482759x + -0.1724137931 + x2 = 0 + -0.1724137931 Reorder the terms: 0.1724137931 + -0.1724137931 + -1.034482759x + x2 = 0 + -0.1724137931 Combine like terms: 0.1724137931 + -0.1724137931 = 0.0000000000 0.0000000000 + -1.034482759x + x2 = 0 + -0.1724137931 -1.034482759x + x2 = 0 + -0.1724137931 Combine like terms: 0 + -0.1724137931 = -0.1724137931 -1.034482759x + x2 = -0.1724137931 The x term is -1.034482759x. Take half its coefficient (-0.5172413795). Square it (0.2675386447) and add it to both sides. Add '0.2675386447' to each side of the equation. -1.034482759x + 0.2675386447 + x2 = -0.1724137931 + 0.2675386447 Reorder the terms: 0.2675386447 + -1.034482759x + x2 = -0.1724137931 + 0.2675386447 Combine like terms: -0.1724137931 + 0.2675386447 = 0.0951248516 0.2675386447 + -1.034482759x + x2 = 0.0951248516 Factor a perfect square on the left side: (x + -0.5172413795)(x + -0.5172413795) = 0.0951248516 Calculate the square root of the right side: 0.30842317 Break this problem into two subproblems by setting (x + -0.5172413795) equal to 0.30842317 and -0.30842317.Subproblem 1
x + -0.5172413795 = 0.30842317 Simplifying x + -0.5172413795 = 0.30842317 Reorder the terms: -0.5172413795 + x = 0.30842317 Solving -0.5172413795 + x = 0.30842317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5172413795' to each side of the equation. -0.5172413795 + 0.5172413795 + x = 0.30842317 + 0.5172413795 Combine like terms: -0.5172413795 + 0.5172413795 = 0.0000000000 0.0000000000 + x = 0.30842317 + 0.5172413795 x = 0.30842317 + 0.5172413795 Combine like terms: 0.30842317 + 0.5172413795 = 0.8256645495 x = 0.8256645495 Simplifying x = 0.8256645495Subproblem 2
x + -0.5172413795 = -0.30842317 Simplifying x + -0.5172413795 = -0.30842317 Reorder the terms: -0.5172413795 + x = -0.30842317 Solving -0.5172413795 + x = -0.30842317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5172413795' to each side of the equation. -0.5172413795 + 0.5172413795 + x = -0.30842317 + 0.5172413795 Combine like terms: -0.5172413795 + 0.5172413795 = 0.0000000000 0.0000000000 + x = -0.30842317 + 0.5172413795 x = -0.30842317 + 0.5172413795 Combine like terms: -0.30842317 + 0.5172413795 = 0.2088182095 x = 0.2088182095 Simplifying x = 0.2088182095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8256645495, 0.2088182095}
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