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Simplifying 3(3x + 12) = 4x2 Reorder the terms: 3(12 + 3x) = 4x2 (12 * 3 + 3x * 3) = 4x2 (36 + 9x) = 4x2 Solving 36 + 9x = 4x2 Solving for variable 'x'. Combine like terms: 4x2 + -4x2 = 0 36 + 9x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -9 + -2.25x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.25x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.25x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.25x + x2 = 0 + 9 -2.25x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.25x + x2 = 9 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 9 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 9 + 1.265625 Combine like terms: 9 + 1.265625 = 10.265625 1.265625 + -2.25x + x2 = 10.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + -1.125) equal to 3.204001404 and -3.204001404.Subproblem 1
x + -1.125 = 3.204001404 Simplifying x + -1.125 = 3.204001404 Reorder the terms: -1.125 + x = 3.204001404 Solving -1.125 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 3.204001404 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 3.204001404 + 1.125 x = 3.204001404 + 1.125 Combine like terms: 3.204001404 + 1.125 = 4.329001404 x = 4.329001404 Simplifying x = 4.329001404Subproblem 2
x + -1.125 = -3.204001404 Simplifying x + -1.125 = -3.204001404 Reorder the terms: -1.125 + x = -3.204001404 Solving -1.125 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -3.204001404 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -3.204001404 + 1.125 x = -3.204001404 + 1.125 Combine like terms: -3.204001404 + 1.125 = -2.079001404 x = -2.079001404 Simplifying x = -2.079001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.329001404, -2.079001404}
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