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Simplifying 0.5(x + 6)(x) + -56 = 0 Reorder the terms: 0.5(6 + x)(x) + -56 = 0 Reorder the terms for easier multiplication: 0.5x(6 + x) + -56 = 0 (6 * 0.5x + x * 0.5x) + -56 = 0 (3x + 0.5x2) + -56 = 0 Reorder the terms: -56 + 3x + 0.5x2 = 0 Solving -56 + 3x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -112 + 6x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + 6x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 6x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 6x + x2 = 0 + 112 6x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 6x + x2 = 112 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 = 112 + 9 Reorder the terms: 9 + 6x + x2 = 112 + 9 Combine like terms: 112 + 9 = 121 9 + 6x + x2 = 121 Factor a perfect square on the left side: (x + 3)(x + 3) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (x + 3) equal to 11 and -11.Subproblem 1
x + 3 = 11 Simplifying x + 3 = 11 Reorder the terms: 3 + x = 11 Solving 3 + x = 11 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 = 11 + -3 Combine like terms: 3 + -3 = 0 0 + x = 11 + -3 x = 11 + -3 Combine like terms: 11 + -3 = 8 x = 8 Simplifying x = 8Subproblem 2
x + 3 = -11 Simplifying x + 3 = -11 Reorder the terms: 3 + x = -11 Solving 3 + x = -11 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 = -11 + -3 Combine like terms: 3 + -3 = 0 0 + x = -11 + -3 x = -11 + -3 Combine like terms: -11 + -3 = -14 x = -14 Simplifying x = -14Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, -14}
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