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Simplifying 2 = 0.6x2 + 3x + 4 Reorder the terms: 2 = 4 + 3x + 0.6x2 Solving 2 = 4 + 3x + 0.6x2 Solving for variable 'x'. Combine like terms: 2 + -4 = -2 -2 + -3x + -0.6x2 = 4 + 3x + 0.6x2 + -4 + -3x + -0.6x2 Reorder the terms: -2 + -3x + -0.6x2 = 4 + -4 + 3x + -3x + 0.6x2 + -0.6x2 Combine like terms: 4 + -4 = 0 -2 + -3x + -0.6x2 = 0 + 3x + -3x + 0.6x2 + -0.6x2 -2 + -3x + -0.6x2 = 3x + -3x + 0.6x2 + -0.6x2 Combine like terms: 3x + -3x = 0 -2 + -3x + -0.6x2 = 0 + 0.6x2 + -0.6x2 -2 + -3x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 -2 + -3x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. 3.333333333 + 5x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 5x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 5x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 5x + x2 = 0 + -3.333333333 5x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 5x + x2 = -3.333333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -3.333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -3.333333333 + 6.25 Combine like terms: -3.333333333 + 6.25 = 2.916666667 6.25 + 5x + x2 = 2.916666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2.916666667 Calculate the square root of the right side: 1.707825128 Break this problem into two subproblems by setting (x + 2.5) equal to 1.707825128 and -1.707825128.Subproblem 1
x + 2.5 = 1.707825128 Simplifying x + 2.5 = 1.707825128 Reorder the terms: 2.5 + x = 1.707825128 Solving 2.5 + x = 1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.707825128 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.707825128 + -2.5 x = 1.707825128 + -2.5 Combine like terms: 1.707825128 + -2.5 = -0.792174872 x = -0.792174872 Simplifying x = -0.792174872Subproblem 2
x + 2.5 = -1.707825128 Simplifying x + 2.5 = -1.707825128 Reorder the terms: 2.5 + x = -1.707825128 Solving 2.5 + x = -1.707825128 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.707825128 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.707825128 + -2.5 x = -1.707825128 + -2.5 Combine like terms: -1.707825128 + -2.5 = -4.207825128 x = -4.207825128 Simplifying x = -4.207825128Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.792174872, -4.207825128}
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