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Simplifying -1x2 + 6x = -30 Reorder the terms: 6x + -1x2 = -30 Solving 6x + -1x2 = -30 Solving for variable 'x'. Reorder the terms: 30 + 6x + -1x2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + -6x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + -6x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -6x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -6x + x2 = 0 + 30 -6x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -6x + x2 = 30 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 = 30 + 9 Reorder the terms: 9 + -6x + x2 = 30 + 9 Combine like terms: 30 + 9 = 39 9 + -6x + x2 = 39 Factor a perfect square on the left side: (x + -3)(x + -3) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + -3) equal to 6.244997998 and -6.244997998.Subproblem 1
x + -3 = 6.244997998 Simplifying x + -3 = 6.244997998 Reorder the terms: -3 + x = 6.244997998 Solving -3 + x = 6.244997998 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 = 6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.244997998 + 3 x = 6.244997998 + 3 Combine like terms: 6.244997998 + 3 = 9.244997998 x = 9.244997998 Simplifying x = 9.244997998Subproblem 2
x + -3 = -6.244997998 Simplifying x + -3 = -6.244997998 Reorder the terms: -3 + x = -6.244997998 Solving -3 + x = -6.244997998 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 = -6.244997998 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.244997998 + 3 x = -6.244997998 + 3 Combine like terms: -6.244997998 + 3 = -3.244997998 x = -3.244997998 Simplifying x = -3.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.244997998, -3.244997998}
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