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Simplifying (3x2 + -4x + -46) + (3x2 + 7x) = 0 Reorder the terms: (-46 + -4x + 3x2) + (3x2 + 7x) = 0 Remove parenthesis around (-46 + -4x + 3x2) -46 + -4x + 3x2 + (3x2 + 7x) = 0 Reorder the terms: -46 + -4x + 3x2 + (7x + 3x2) = 0 Remove parenthesis around (7x + 3x2) -46 + -4x + 3x2 + 7x + 3x2 = 0 Reorder the terms: -46 + -4x + 7x + 3x2 + 3x2 = 0 Combine like terms: -4x + 7x = 3x -46 + 3x + 3x2 + 3x2 = 0 Combine like terms: 3x2 + 3x2 = 6x2 -46 + 3x + 6x2 = 0 Solving -46 + 3x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -7.666666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + 0.5x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + 0.5x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 7.666666667 0.5x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 0.5x + x2 = 7.666666667 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 7.666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 7.666666667 + 0.0625 Combine like terms: 7.666666667 + 0.0625 = 7.729166667 0.0625 + 0.5x + x2 = 7.729166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 7.729166667 Calculate the square root of the right side: 2.780137886 Break this problem into two subproblems by setting (x + 0.25) equal to 2.780137886 and -2.780137886.Subproblem 1
x + 0.25 = 2.780137886 Simplifying x + 0.25 = 2.780137886 Reorder the terms: 0.25 + x = 2.780137886 Solving 0.25 + x = 2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.780137886 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.780137886 + -0.25 x = 2.780137886 + -0.25 Combine like terms: 2.780137886 + -0.25 = 2.530137886 x = 2.530137886 Simplifying x = 2.530137886Subproblem 2
x + 0.25 = -2.780137886 Simplifying x + 0.25 = -2.780137886 Reorder the terms: 0.25 + x = -2.780137886 Solving 0.25 + x = -2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.780137886 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.780137886 + -0.25 x = -2.780137886 + -0.25 Combine like terms: -2.780137886 + -0.25 = -3.030137886 x = -3.030137886 Simplifying x = -3.030137886Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.530137886, -3.030137886}
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