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Simplifying 44x2 + 125x + -4 = 4 Reorder the terms: -4 + 125x + 44x2 = 4 Solving -4 + 125x + 44x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -4 + 125x + 44x2 = 4 + -4 Combine like terms: -4 + -4 = -8 -8 + 125x + 44x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -8 + 125x + 44x2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.1818181818 + 2.840909091x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + 2.840909091x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + 2.840909091x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + 2.840909091x + x2 = 0 + 0.1818181818 2.840909091x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 2.840909091x + x2 = 0.1818181818 The x term is 2.840909091x. Take half its coefficient (1.420454546). Square it (2.017691117) and add it to both sides. Add '2.017691117' to each side of the equation. 2.840909091x + 2.017691117 + x2 = 0.1818181818 + 2.017691117 Reorder the terms: 2.017691117 + 2.840909091x + x2 = 0.1818181818 + 2.017691117 Combine like terms: 0.1818181818 + 2.017691117 = 2.1995092988 2.017691117 + 2.840909091x + x2 = 2.1995092988 Factor a perfect square on the left side: (x + 1.420454546)(x + 1.420454546) = 2.1995092988 Calculate the square root of the right side: 1.483074273 Break this problem into two subproblems by setting (x + 1.420454546) equal to 1.483074273 and -1.483074273.Subproblem 1
x + 1.420454546 = 1.483074273 Simplifying x + 1.420454546 = 1.483074273 Reorder the terms: 1.420454546 + x = 1.483074273 Solving 1.420454546 + x = 1.483074273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.420454546' to each side of the equation. 1.420454546 + -1.420454546 + x = 1.483074273 + -1.420454546 Combine like terms: 1.420454546 + -1.420454546 = 0.000000000 0.000000000 + x = 1.483074273 + -1.420454546 x = 1.483074273 + -1.420454546 Combine like terms: 1.483074273 + -1.420454546 = 0.062619727 x = 0.062619727 Simplifying x = 0.062619727Subproblem 2
x + 1.420454546 = -1.483074273 Simplifying x + 1.420454546 = -1.483074273 Reorder the terms: 1.420454546 + x = -1.483074273 Solving 1.420454546 + x = -1.483074273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.420454546' to each side of the equation. 1.420454546 + -1.420454546 + x = -1.483074273 + -1.420454546 Combine like terms: 1.420454546 + -1.420454546 = 0.000000000 0.000000000 + x = -1.483074273 + -1.420454546 x = -1.483074273 + -1.420454546 Combine like terms: -1.483074273 + -1.420454546 = -2.903528819 x = -2.903528819 Simplifying x = -2.903528819Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062619727, -2.903528819}
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