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Simplifying 6x2 + -16 + 3x = 0 Reorder the terms: -16 + 3x + 6x2 = 0 Solving -16 + 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'. -2.666666667 + 0.5x + x2 = 0 Move the constant term to the right: Add '2.666666667' to each side of the equation. -2.666666667 + 0.5x + 2.666666667 + x2 = 0 + 2.666666667 Reorder the terms: -2.666666667 + 2.666666667 + 0.5x + x2 = 0 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 2.666666667 0.5x + x2 = 0 + 2.666666667 Combine like terms: 0 + 2.666666667 = 2.666666667 0.5x + x2 = 2.666666667 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 = 2.666666667 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 2.666666667 + 0.0625 Combine like terms: 2.666666667 + 0.0625 = 2.729166667 0.0625 + 0.5x + x2 = 2.729166667 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 2.729166667 Calculate the square root of the right side: 1.652018967 Break this problem into two subproblems by setting (x + 0.25) equal to 1.652018967 and -1.652018967.Subproblem 1
x + 0.25 = 1.652018967 Simplifying x + 0.25 = 1.652018967 Reorder the terms: 0.25 + x = 1.652018967 Solving 0.25 + x = 1.652018967 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 = 1.652018967 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.652018967 + -0.25 x = 1.652018967 + -0.25 Combine like terms: 1.652018967 + -0.25 = 1.402018967 x = 1.402018967 Simplifying x = 1.402018967Subproblem 2
x + 0.25 = -1.652018967 Simplifying x + 0.25 = -1.652018967 Reorder the terms: 0.25 + x = -1.652018967 Solving 0.25 + x = -1.652018967 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 = -1.652018967 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.652018967 + -0.25 x = -1.652018967 + -0.25 Combine like terms: -1.652018967 + -0.25 = -1.902018967 x = -1.902018967 Simplifying x = -1.902018967Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.402018967, -1.902018967}
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