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Simplifying 5x2 + 48x2 + 100x + 2 = 0 Reorder the terms: 2 + 100x + 5x2 + 48x2 = 0 Combine like terms: 5x2 + 48x2 = 53x2 2 + 100x + 53x2 = 0 Solving 2 + 100x + 53x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. 0.03773584906 + 1.886792453x + x2 = 0 Move the constant term to the right: Add '-0.03773584906' to each side of the equation. 0.03773584906 + 1.886792453x + -0.03773584906 + x2 = 0 + -0.03773584906 Reorder the terms: 0.03773584906 + -0.03773584906 + 1.886792453x + x2 = 0 + -0.03773584906 Combine like terms: 0.03773584906 + -0.03773584906 = 0.00000000000 0.00000000000 + 1.886792453x + x2 = 0 + -0.03773584906 1.886792453x + x2 = 0 + -0.03773584906 Combine like terms: 0 + -0.03773584906 = -0.03773584906 1.886792453x + x2 = -0.03773584906 The x term is 1.886792453x. Take half its coefficient (0.9433962265). Square it (0.8899964402) and add it to both sides. Add '0.8899964402' to each side of the equation. 1.886792453x + 0.8899964402 + x2 = -0.03773584906 + 0.8899964402 Reorder the terms: 0.8899964402 + 1.886792453x + x2 = -0.03773584906 + 0.8899964402 Combine like terms: -0.03773584906 + 0.8899964402 = 0.85226059114 0.8899964402 + 1.886792453x + x2 = 0.85226059114 Factor a perfect square on the left side: (x + 0.9433962265)(x + 0.9433962265) = 0.85226059114 Calculate the square root of the right side: 0.923179609 Break this problem into two subproblems by setting (x + 0.9433962265) equal to 0.923179609 and -0.923179609.Subproblem 1
x + 0.9433962265 = 0.923179609 Simplifying x + 0.9433962265 = 0.923179609 Reorder the terms: 0.9433962265 + x = 0.923179609 Solving 0.9433962265 + x = 0.923179609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9433962265' to each side of the equation. 0.9433962265 + -0.9433962265 + x = 0.923179609 + -0.9433962265 Combine like terms: 0.9433962265 + -0.9433962265 = 0.0000000000 0.0000000000 + x = 0.923179609 + -0.9433962265 x = 0.923179609 + -0.9433962265 Combine like terms: 0.923179609 + -0.9433962265 = -0.0202166175 x = -0.0202166175 Simplifying x = -0.0202166175Subproblem 2
x + 0.9433962265 = -0.923179609 Simplifying x + 0.9433962265 = -0.923179609 Reorder the terms: 0.9433962265 + x = -0.923179609 Solving 0.9433962265 + x = -0.923179609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9433962265' to each side of the equation. 0.9433962265 + -0.9433962265 + x = -0.923179609 + -0.9433962265 Combine like terms: 0.9433962265 + -0.9433962265 = 0.0000000000 0.0000000000 + x = -0.923179609 + -0.9433962265 x = -0.923179609 + -0.9433962265 Combine like terms: -0.923179609 + -0.9433962265 = -1.8665758355 x = -1.8665758355 Simplifying x = -1.8665758355Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0202166175, -1.8665758355}
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