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Simplifying 11 = 6x2 + -30x + -36 Reorder the terms: 11 = -36 + -30x + 6x2 Solving 11 = -36 + -30x + 6x2 Solving for variable 'x'. Combine like terms: 11 + 36 = 47 47 + 30x + -6x2 = -36 + -30x + 6x2 + 36 + 30x + -6x2 Reorder the terms: 47 + 30x + -6x2 = -36 + 36 + -30x + 30x + 6x2 + -6x2 Combine like terms: -36 + 36 = 0 47 + 30x + -6x2 = 0 + -30x + 30x + 6x2 + -6x2 47 + 30x + -6x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 47 + 30x + -6x2 = 0 + 6x2 + -6x2 47 + 30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 47 + 30x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -7.833333333 + -5x + x2 = 0 Move the constant term to the right: Add '7.833333333' to each side of the equation. -7.833333333 + -5x + 7.833333333 + x2 = 0 + 7.833333333 Reorder the terms: -7.833333333 + 7.833333333 + -5x + x2 = 0 + 7.833333333 Combine like terms: -7.833333333 + 7.833333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + 7.833333333 -5x + x2 = 0 + 7.833333333 Combine like terms: 0 + 7.833333333 = 7.833333333 -5x + x2 = 7.833333333 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 7.833333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7.833333333 + 6.25 Combine like terms: 7.833333333 + 6.25 = 14.083333333 6.25 + -5x + x2 = 14.083333333 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 14.083333333 Calculate the square root of the right side: 3.75277675 Break this problem into two subproblems by setting (x + -2.5) equal to 3.75277675 and -3.75277675.Subproblem 1
x + -2.5 = 3.75277675 Simplifying x + -2.5 = 3.75277675 Reorder the terms: -2.5 + x = 3.75277675 Solving -2.5 + x = 3.75277675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.75277675 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.75277675 + 2.5 x = 3.75277675 + 2.5 Combine like terms: 3.75277675 + 2.5 = 6.25277675 x = 6.25277675 Simplifying x = 6.25277675Subproblem 2
x + -2.5 = -3.75277675 Simplifying x + -2.5 = -3.75277675 Reorder the terms: -2.5 + x = -3.75277675 Solving -2.5 + x = -3.75277675 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.75277675 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.75277675 + 2.5 x = -3.75277675 + 2.5 Combine like terms: -3.75277675 + 2.5 = -1.25277675 x = -1.25277675 Simplifying x = -1.25277675Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.25277675, -1.25277675}
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