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Simplifying 121x2 + -110x = 4 Reorder the terms: -110x + 121x2 = 4 Solving -110x + 121x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + -110x + 121x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -110x + 121x2 = 0 Begin completing the square. Divide all terms by 121 the coefficient of the squared term: Divide each side by '121'. -0.03305785124 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '0.03305785124' to each side of the equation. -0.03305785124 + -0.9090909091x + 0.03305785124 + x2 = 0 + 0.03305785124 Reorder the terms: -0.03305785124 + 0.03305785124 + -0.9090909091x + x2 = 0 + 0.03305785124 Combine like terms: -0.03305785124 + 0.03305785124 = 0.00000000000 0.00000000000 + -0.9090909091x + x2 = 0 + 0.03305785124 -0.9090909091x + x2 = 0 + 0.03305785124 Combine like terms: 0 + 0.03305785124 = 0.03305785124 -0.9090909091x + x2 = 0.03305785124 The x term is -0.9090909091x. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091x + 0.2066115703 + x2 = 0.03305785124 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = 0.03305785124 + 0.2066115703 Combine like terms: 0.03305785124 + 0.2066115703 = 0.23966942154 0.2066115703 + -0.9090909091x + x2 = 0.23966942154 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = 0.23966942154 Calculate the square root of the right side: 0.489560437 Break this problem into two subproblems by setting (x + -0.4545454546) equal to 0.489560437 and -0.489560437.Subproblem 1
x + -0.4545454546 = 0.489560437 Simplifying x + -0.4545454546 = 0.489560437 Reorder the terms: -0.4545454546 + x = 0.489560437 Solving -0.4545454546 + x = 0.489560437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = 0.489560437 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = 0.489560437 + 0.4545454546 x = 0.489560437 + 0.4545454546 Combine like terms: 0.489560437 + 0.4545454546 = 0.9441058916 x = 0.9441058916 Simplifying x = 0.9441058916Subproblem 2
x + -0.4545454546 = -0.489560437 Simplifying x + -0.4545454546 = -0.489560437 Reorder the terms: -0.4545454546 + x = -0.489560437 Solving -0.4545454546 + x = -0.489560437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = -0.489560437 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = -0.489560437 + 0.4545454546 x = -0.489560437 + 0.4545454546 Combine like terms: -0.489560437 + 0.4545454546 = -0.0350149824 x = -0.0350149824 Simplifying x = -0.0350149824Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9441058916, -0.0350149824}
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