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Simplifying 16x2 + -3 + 6x + -4x2 + -10 = 0 Reorder the terms: -3 + -10 + 6x + 16x2 + -4x2 = 0 Combine like terms: -3 + -10 = -13 -13 + 6x + 16x2 + -4x2 = 0 Combine like terms: 16x2 + -4x2 = 12x2 -13 + 6x + 12x2 = 0 Solving -13 + 6x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.083333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.083333333' to each side of the equation. -1.083333333 + 0.5x + 1.083333333 + x2 = 0 + 1.083333333 Reorder the terms: -1.083333333 + 1.083333333 + 0.5x + x2 = 0 + 1.083333333 Combine like terms: -1.083333333 + 1.083333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 1.083333333 0.5x + x2 = 0 + 1.083333333 Combine like terms: 0 + 1.083333333 = 1.083333333 0.5x + x2 = 1.083333333 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 = 1.083333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.083333333 + 0.0625 Combine like terms: 1.083333333 + 0.0625 = 1.145833333 0.0625 + 0.5x + x2 = 1.145833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.145833333 Calculate the square root of the right side: 1.070436048 Break this problem into two subproblems by setting (x + 0.25) equal to 1.070436048 and -1.070436048.Subproblem 1
x + 0.25 = 1.070436048 Simplifying x + 0.25 = 1.070436048 Reorder the terms: 0.25 + x = 1.070436048 Solving 0.25 + x = 1.070436048 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 = 1.070436048 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.070436048 + -0.25 x = 1.070436048 + -0.25 Combine like terms: 1.070436048 + -0.25 = 0.820436048 x = 0.820436048 Simplifying x = 0.820436048Subproblem 2
x + 0.25 = -1.070436048 Simplifying x + 0.25 = -1.070436048 Reorder the terms: 0.25 + x = -1.070436048 Solving 0.25 + x = -1.070436048 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 = -1.070436048 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.070436048 + -0.25 x = -1.070436048 + -0.25 Combine like terms: -1.070436048 + -0.25 = -1.320436048 x = -1.320436048 Simplifying x = -1.320436048Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.820436048, -1.320436048}
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