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Simplifying -1x2 + 12x = -21 Reorder the terms: 12x + -1x2 = -21 Solving 12x + -1x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + 12x + -1x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + -12x + x2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + -12x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + -12x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -12x + x2 = 0 + 21 -12x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 -12x + x2 = 21 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 21 + 36 Reorder the terms: 36 + -12x + x2 = 21 + 36 Combine like terms: 21 + 36 = 57 36 + -12x + x2 = 57 Factor a perfect square on the left side: (x + -6)(x + -6) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -6) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -6 = 7.549834435 Simplifying x + -6 = 7.549834435 Reorder the terms: -6 + x = 7.549834435 Solving -6 + x = 7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.549834435 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.549834435 + 6 x = 7.549834435 + 6 Combine like terms: 7.549834435 + 6 = 13.549834435 x = 13.549834435 Simplifying x = 13.549834435Subproblem 2
x + -6 = -7.549834435 Simplifying x + -6 = -7.549834435 Reorder the terms: -6 + x = -7.549834435 Solving -6 + x = -7.549834435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.549834435 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.549834435 + 6 x = -7.549834435 + 6 Combine like terms: -7.549834435 + 6 = -1.549834435 x = -1.549834435 Simplifying x = -1.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.549834435, -1.549834435}
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