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Simplifying 31 + 6x = 2x(-1x + -6) Reorder the terms: 31 + 6x = 2x(-6 + -1x) 31 + 6x = (-6 * 2x + -1x * 2x) 31 + 6x = (-12x + -2x2) Solving 31 + 6x = -12x + -2x2 Solving for variable 'x'. Combine like terms: 6x + 12x = 18x 31 + 18x + 2x2 = -12x + -2x2 + 12x + 2x2 Reorder the terms: 31 + 18x + 2x2 = -12x + 12x + -2x2 + 2x2 Combine like terms: -12x + 12x = 0 31 + 18x + 2x2 = 0 + -2x2 + 2x2 31 + 18x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 31 + 18x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 15.5 + 9x + x2 = 0 Move the constant term to the right: Add '-15.5' to each side of the equation. 15.5 + 9x + -15.5 + x2 = 0 + -15.5 Reorder the terms: 15.5 + -15.5 + 9x + x2 = 0 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + 9x + x2 = 0 + -15.5 9x + x2 = 0 + -15.5 Combine like terms: 0 + -15.5 = -15.5 9x + x2 = -15.5 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -15.5 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -15.5 + 20.25 Combine like terms: -15.5 + 20.25 = 4.75 20.25 + 9x + x2 = 4.75 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 4.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 4.5 = 2.179449472 Simplifying x + 4.5 = 2.179449472 Reorder the terms: 4.5 + x = 2.179449472 Solving 4.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 2.179449472 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 2.179449472 + -4.5 x = 2.179449472 + -4.5 Combine like terms: 2.179449472 + -4.5 = -2.320550528 x = -2.320550528 Simplifying x = -2.320550528Subproblem 2
x + 4.5 = -2.179449472 Simplifying x + 4.5 = -2.179449472 Reorder the terms: 4.5 + x = -2.179449472 Solving 4.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -2.179449472 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -2.179449472 + -4.5 x = -2.179449472 + -4.5 Combine like terms: -2.179449472 + -4.5 = -6.679449472 x = -6.679449472 Simplifying x = -6.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.320550528, -6.679449472}
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