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Simplifying x(x + -6) = 56 Reorder the terms: x(-6 + x) = 56 (-6 * x + x * x) = 56 (-6x + x2) = 56 Solving -6x + x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + -6x + x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -6x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -6x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -6x + x2 = 0 + 56 -6x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -6x + x2 = 56 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 56 + 9 Reorder the terms: 9 + -6x + x2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + -6x + x2 = 65 Factor a perfect square on the left side: (x + -3)(x + -3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (x + -3) equal to 8.062257748 and -8.062257748.Subproblem 1
x + -3 = 8.062257748 Simplifying x + -3 = 8.062257748 Reorder the terms: -3 + x = 8.062257748 Solving -3 + x = 8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 8.062257748 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.062257748 + 3 x = 8.062257748 + 3 Combine like terms: 8.062257748 + 3 = 11.062257748 x = 11.062257748 Simplifying x = 11.062257748Subproblem 2
x + -3 = -8.062257748 Simplifying x + -3 = -8.062257748 Reorder the terms: -3 + x = -8.062257748 Solving -3 + x = -8.062257748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -8.062257748 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.062257748 + 3 x = -8.062257748 + 3 Combine like terms: -8.062257748 + 3 = -5.062257748 x = -5.062257748 Simplifying x = -5.062257748Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.062257748, -5.062257748}
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