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Simplifying x(12 + 2x) = 63 (12 * x + 2x * x) = 63 (12x + 2x2) = 63 Solving 12x + 2x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + 12x + 2x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + 6x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + 6x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + 6x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + 6x + x2 = 0 + 31.5 6x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 6x + x2 = 31.5 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 = 31.5 + 9 Reorder the terms: 9 + 6x + x2 = 31.5 + 9 Combine like terms: 31.5 + 9 = 40.5 9 + 6x + x2 = 40.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (x + 3) equal to 6.363961031 and -6.363961031.Subproblem 1
x + 3 = 6.363961031 Simplifying x + 3 = 6.363961031 Reorder the terms: 3 + x = 6.363961031 Solving 3 + x = 6.363961031 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 = 6.363961031 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.363961031 + -3 x = 6.363961031 + -3 Combine like terms: 6.363961031 + -3 = 3.363961031 x = 3.363961031 Simplifying x = 3.363961031Subproblem 2
x + 3 = -6.363961031 Simplifying x + 3 = -6.363961031 Reorder the terms: 3 + x = -6.363961031 Solving 3 + x = -6.363961031 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 = -6.363961031 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.363961031 + -3 x = -6.363961031 + -3 Combine like terms: -6.363961031 + -3 = -9.363961031 x = -9.363961031 Simplifying x = -9.363961031Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.363961031, -9.363961031}
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