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Simplifying 4.1 = x2 + 3x Reorder the terms: 4.1 = 3x + x2 Solving 4.1 = 3x + x2 Solving for variable 'x'. Reorder the terms: 4.1 + -3x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 4.1 + -3x + -1x2 = 0 + x2 + -1x2 4.1 + -3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4.1 + -3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4.1 + 3x + x2 = 0 Move the constant term to the right: Add '4.1' to each side of the equation. -4.1 + 3x + 4.1 + x2 = 0 + 4.1 Reorder the terms: -4.1 + 4.1 + 3x + x2 = 0 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + 3x + x2 = 0 + 4.1 3x + x2 = 0 + 4.1 Combine like terms: 0 + 4.1 = 4.1 3x + x2 = 4.1 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 4.1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 4.1 + 2.25 Combine like terms: 4.1 + 2.25 = 6.35 2.25 + 3x + x2 = 6.35 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 6.35 Calculate the square root of the right side: 2.519920634 Break this problem into two subproblems by setting (x + 1.5) equal to 2.519920634 and -2.519920634.Subproblem 1
x + 1.5 = 2.519920634 Simplifying x + 1.5 = 2.519920634 Reorder the terms: 1.5 + x = 2.519920634 Solving 1.5 + x = 2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.519920634 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.519920634 + -1.5 x = 2.519920634 + -1.5 Combine like terms: 2.519920634 + -1.5 = 1.019920634 x = 1.019920634 Simplifying x = 1.019920634Subproblem 2
x + 1.5 = -2.519920634 Simplifying x + 1.5 = -2.519920634 Reorder the terms: 1.5 + x = -2.519920634 Solving 1.5 + x = -2.519920634 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.519920634 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.519920634 + -1.5 x = -2.519920634 + -1.5 Combine like terms: -2.519920634 + -1.5 = -4.019920634 x = -4.019920634 Simplifying x = -4.019920634Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.019920634, -4.019920634}
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