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Simplifying 6(x2 + -2) + 1 + -16 + x = 0 Reorder the terms: 6(-2 + x2) + 1 + -16 + x = 0 (-2 * 6 + x2 * 6) + 1 + -16 + x = 0 (-12 + 6x2) + 1 + -16 + x = 0 Reorder the terms: -12 + 1 + -16 + x + 6x2 = 0 Combine like terms: -12 + 1 = -11 -11 + -16 + x + 6x2 = 0 Combine like terms: -11 + -16 = -27 -27 + x + 6x2 = 0 Solving -27 + x + 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'. -4.5 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 0.1666666667x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 0.1666666667x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 0.1666666667x + x2 = 0 + 4.5 0.1666666667x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 0.1666666667x + x2 = 4.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1666666667x + 0.25 + x2 = 4.5 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + 0.1666666667x + x2 = 4.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 0.5 = 2.179449472 Simplifying x + 0.5 = 2.179449472 Reorder the terms: 0.5 + x = 2.179449472 Solving 0.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.179449472 + -0.5 x = 2.179449472 + -0.5 Combine like terms: 2.179449472 + -0.5 = 1.679449472 x = 1.679449472 Simplifying x = 1.679449472Subproblem 2
x + 0.5 = -2.179449472 Simplifying x + 0.5 = -2.179449472 Reorder the terms: 0.5 + x = -2.179449472 Solving 0.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.179449472 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.179449472 + -0.5 x = -2.179449472 + -0.5 Combine like terms: -2.179449472 + -0.5 = -2.679449472 x = -2.679449472 Simplifying x = -2.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.679449472, -2.679449472}
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