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Simplifying 0 = -0.3334x * x + -2x + 2.3334 Multiply x * x 0 = -0.3334x2 + -2x + 2.3334 Reorder the terms: 0 = 2.3334 + -2x + -0.3334x2 Solving 0 = 2.3334 + -2x + -0.3334x2 Solving for variable 'x'. Combine like terms: 0 + -2.3334 = -2.3334 -2.3334 + 2x + 0.3334x2 = 2.3334 + -2x + -0.3334x2 + -2.3334 + 2x + 0.3334x2 Reorder the terms: -2.3334 + 2x + 0.3334x2 = 2.3334 + -2.3334 + -2x + 2x + -0.3334x2 + 0.3334x2 Combine like terms: 2.3334 + -2.3334 = 0.0000 -2.3334 + 2x + 0.3334x2 = 0.0000 + -2x + 2x + -0.3334x2 + 0.3334x2 -2.3334 + 2x + 0.3334x2 = -2x + 2x + -0.3334x2 + 0.3334x2 Combine like terms: -2x + 2x = 0 -2.3334 + 2x + 0.3334x2 = 0 + -0.3334x2 + 0.3334x2 -2.3334 + 2x + 0.3334x2 = -0.3334x2 + 0.3334x2 Combine like terms: -0.3334x2 + 0.3334x2 = 0.0000 -2.3334 + 2x + 0.3334x2 = 0.0000 Begin completing the square. Divide all terms by 0.3334 the coefficient of the squared term: Divide each side by '0.3334'. -6.99880024 + 5.99880024x + x2 = 0 Move the constant term to the right: Add '6.99880024' to each side of the equation. -6.99880024 + 5.99880024x + 6.99880024 + x2 = 0 + 6.99880024 Reorder the terms: -6.99880024 + 6.99880024 + 5.99880024x + x2 = 0 + 6.99880024 Combine like terms: -6.99880024 + 6.99880024 = 0.00000000 0.00000000 + 5.99880024x + x2 = 0 + 6.99880024 5.99880024x + x2 = 0 + 6.99880024 Combine like terms: 0 + 6.99880024 = 6.99880024 5.99880024x + x2 = 6.99880024 The x term is 5.99880024x. Take half its coefficient (2.99940012). Square it (8.996401080) and add it to both sides. Add '8.996401080' to each side of the equation. 5.99880024x + 8.996401080 + x2 = 6.99880024 + 8.996401080 Reorder the terms: 8.996401080 + 5.99880024x + x2 = 6.99880024 + 8.996401080 Combine like terms: 6.99880024 + 8.996401080 = 15.99520132 8.996401080 + 5.99880024x + x2 = 15.99520132 Factor a perfect square on the left side: (x + 2.99940012)(x + 2.99940012) = 15.99520132 Calculate the square root of the right side: 3.99940012 Break this problem into two subproblems by setting (x + 2.99940012) equal to 3.99940012 and -3.99940012.Subproblem 1
x + 2.99940012 = 3.99940012 Simplifying x + 2.99940012 = 3.99940012 Reorder the terms: 2.99940012 + x = 3.99940012 Solving 2.99940012 + x = 3.99940012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.99940012' to each side of the equation. 2.99940012 + -2.99940012 + x = 3.99940012 + -2.99940012 Combine like terms: 2.99940012 + -2.99940012 = 0.00000000 0.00000000 + x = 3.99940012 + -2.99940012 x = 3.99940012 + -2.99940012 Combine like terms: 3.99940012 + -2.99940012 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 2.99940012 = -3.99940012 Simplifying x + 2.99940012 = -3.99940012 Reorder the terms: 2.99940012 + x = -3.99940012 Solving 2.99940012 + x = -3.99940012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.99940012' to each side of the equation. 2.99940012 + -2.99940012 + x = -3.99940012 + -2.99940012 Combine like terms: 2.99940012 + -2.99940012 = 0.00000000 0.00000000 + x = -3.99940012 + -2.99940012 x = -3.99940012 + -2.99940012 Combine like terms: -3.99940012 + -2.99940012 = -6.99880024 x = -6.99880024 Simplifying x = -6.99880024Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -6.99880024}
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