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Simplifying x(x + -6) = 71 Reorder the terms: x(-6 + x) = 71 (-6 * x + x * x) = 71 (-6x + x2) = 71 Solving -6x + x2 = 71 Solving for variable 'x'. Reorder the terms: -71 + -6x + x2 = 71 + -71 Combine like terms: 71 + -71 = 0 -71 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '71' to each side of the equation. -71 + -6x + 71 + x2 = 0 + 71 Reorder the terms: -71 + 71 + -6x + x2 = 0 + 71 Combine like terms: -71 + 71 = 0 0 + -6x + x2 = 0 + 71 -6x + x2 = 0 + 71 Combine like terms: 0 + 71 = 71 -6x + x2 = 71 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 = 71 + 9 Reorder the terms: 9 + -6x + x2 = 71 + 9 Combine like terms: 71 + 9 = 80 9 + -6x + x2 = 80 Factor a perfect square on the left side: (x + -3)(x + -3) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -3) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -3 = 8.94427191 Simplifying x + -3 = 8.94427191 Reorder the terms: -3 + x = 8.94427191 Solving -3 + x = 8.94427191 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 = 8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.94427191 + 3 x = 8.94427191 + 3 Combine like terms: 8.94427191 + 3 = 11.94427191 x = 11.94427191 Simplifying x = 11.94427191Subproblem 2
x + -3 = -8.94427191 Simplifying x + -3 = -8.94427191 Reorder the terms: -3 + x = -8.94427191 Solving -3 + x = -8.94427191 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 = -8.94427191 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.94427191 + 3 x = -8.94427191 + 3 Combine like terms: -8.94427191 + 3 = -5.94427191 x = -5.94427191 Simplifying x = -5.94427191Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.94427191, -5.94427191}
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