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Simplifying 38x2 + -108x + -225 = 0 Reorder the terms: -225 + -108x + 38x2 = 0 Solving -225 + -108x + 38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 38 the coefficient of the squared term: Divide each side by '38'. -5.921052632 + -2.842105263x + x2 = 0 Move the constant term to the right: Add '5.921052632' to each side of the equation. -5.921052632 + -2.842105263x + 5.921052632 + x2 = 0 + 5.921052632 Reorder the terms: -5.921052632 + 5.921052632 + -2.842105263x + x2 = 0 + 5.921052632 Combine like terms: -5.921052632 + 5.921052632 = 0.000000000 0.000000000 + -2.842105263x + x2 = 0 + 5.921052632 -2.842105263x + x2 = 0 + 5.921052632 Combine like terms: 0 + 5.921052632 = 5.921052632 -2.842105263x + x2 = 5.921052632 The x term is -2.842105263x. Take half its coefficient (-1.421052632). Square it (2.019390583) and add it to both sides. Add '2.019390583' to each side of the equation. -2.842105263x + 2.019390583 + x2 = 5.921052632 + 2.019390583 Reorder the terms: 2.019390583 + -2.842105263x + x2 = 5.921052632 + 2.019390583 Combine like terms: 5.921052632 + 2.019390583 = 7.940443215 2.019390583 + -2.842105263x + x2 = 7.940443215 Factor a perfect square on the left side: (x + -1.421052632)(x + -1.421052632) = 7.940443215 Calculate the square root of the right side: 2.817879205 Break this problem into two subproblems by setting (x + -1.421052632) equal to 2.817879205 and -2.817879205.Subproblem 1
x + -1.421052632 = 2.817879205 Simplifying x + -1.421052632 = 2.817879205 Reorder the terms: -1.421052632 + x = 2.817879205 Solving -1.421052632 + x = 2.817879205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.421052632' to each side of the equation. -1.421052632 + 1.421052632 + x = 2.817879205 + 1.421052632 Combine like terms: -1.421052632 + 1.421052632 = 0.000000000 0.000000000 + x = 2.817879205 + 1.421052632 x = 2.817879205 + 1.421052632 Combine like terms: 2.817879205 + 1.421052632 = 4.238931837 x = 4.238931837 Simplifying x = 4.238931837Subproblem 2
x + -1.421052632 = -2.817879205 Simplifying x + -1.421052632 = -2.817879205 Reorder the terms: -1.421052632 + x = -2.817879205 Solving -1.421052632 + x = -2.817879205 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.421052632' to each side of the equation. -1.421052632 + 1.421052632 + x = -2.817879205 + 1.421052632 Combine like terms: -1.421052632 + 1.421052632 = 0.000000000 0.000000000 + x = -2.817879205 + 1.421052632 x = -2.817879205 + 1.421052632 Combine like terms: -2.817879205 + 1.421052632 = -1.396826573 x = -1.396826573 Simplifying x = -1.396826573Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.238931837, -1.396826573}
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