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Simplifying 3.3 = x2 + x Reorder the terms: 3.3 = x + x2 Solving 3.3 = x + x2 Solving for variable 'x'. Reorder the terms: 3.3 + -1x + -1x2 = x + -1x + x2 + -1x2 Combine like terms: x + -1x = 0 3.3 + -1x + -1x2 = 0 + x2 + -1x2 3.3 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 3.3 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3.3 + x + x2 = 0 Move the constant term to the right: Add '3.3' to each side of the equation. -3.3 + x + 3.3 + x2 = 0 + 3.3 Reorder the terms: -3.3 + 3.3 + x + x2 = 0 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x + x2 = 0 + 3.3 x + x2 = 0 + 3.3 Combine like terms: 0 + 3.3 = 3.3 x + x2 = 3.3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 3.3 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 3.3 + 0.25 Combine like terms: 3.3 + 0.25 = 3.55 1.25 + x2 = 3.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.55 Calculate the square root of the right side: 1.884144368 Break this problem into two subproblems by setting (x + 0.5) equal to 1.884144368 and -1.884144368.Subproblem 1
x + 0.5 = 1.884144368 Simplifying x + 0.5 = 1.884144368 Reorder the terms: 0.5 + x = 1.884144368 Solving 0.5 + x = 1.884144368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.884144368 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.884144368 + -0.5 x = 1.884144368 + -0.5 Combine like terms: 1.884144368 + -0.5 = 1.384144368 x = 1.384144368 Simplifying x = 1.384144368Subproblem 2
x + 0.5 = -1.884144368 Simplifying x + 0.5 = -1.884144368 Reorder the terms: 0.5 + x = -1.884144368 Solving 0.5 + x = -1.884144368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.884144368 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.884144368 + -0.5 x = -1.884144368 + -0.5 Combine like terms: -1.884144368 + -0.5 = -2.384144368 x = -2.384144368 Simplifying x = -2.384144368Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.384144368, -2.384144368}
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