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Simplifying 6x2 + -11x + -13 = 5(x2 + -1) + 3 Reorder the terms: -13 + -11x + 6x2 = 5(x2 + -1) + 3 Reorder the terms: -13 + -11x + 6x2 = 5(-1 + x2) + 3 -13 + -11x + 6x2 = (-1 * 5 + x2 * 5) + 3 -13 + -11x + 6x2 = (-5 + 5x2) + 3 Reorder the terms: -13 + -11x + 6x2 = -5 + 3 + 5x2 Combine like terms: -5 + 3 = -2 -13 + -11x + 6x2 = -2 + 5x2 Solving -13 + -11x + 6x2 = -2 + 5x2 Solving for variable 'x'. Reorder the terms: -13 + 2 + -11x + 6x2 + -5x2 = -2 + 5x2 + 2 + -5x2 Combine like terms: -13 + 2 = -11 -11 + -11x + 6x2 + -5x2 = -2 + 5x2 + 2 + -5x2 Combine like terms: 6x2 + -5x2 = 1x2 -11 + -11x + 1x2 = -2 + 5x2 + 2 + -5x2 Reorder the terms: -11 + -11x + 1x2 = -2 + 2 + 5x2 + -5x2 Combine like terms: -2 + 2 = 0 -11 + -11x + 1x2 = 0 + 5x2 + -5x2 -11 + -11x + 1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -11 + -11x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -11x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -11x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -11x + x2 = 0 + 11 -11x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -11x + x2 = 11 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 11 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 11 + 30.25 Combine like terms: 11 + 30.25 = 41.25 30.25 + -11x + x2 = 41.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -5.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -5.5 = 6.422616289 Simplifying x + -5.5 = 6.422616289 Reorder the terms: -5.5 + x = 6.422616289 Solving -5.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.422616289 + 5.5 x = 6.422616289 + 5.5 Combine like terms: 6.422616289 + 5.5 = 11.922616289 x = 11.922616289 Simplifying x = 11.922616289Subproblem 2
x + -5.5 = -6.422616289 Simplifying x + -5.5 = -6.422616289 Reorder the terms: -5.5 + x = -6.422616289 Solving -5.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.422616289 + 5.5 x = -6.422616289 + 5.5 Combine like terms: -6.422616289 + 5.5 = -0.922616289 x = -0.922616289 Simplifying x = -0.922616289Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.922616289, -0.922616289}
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