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Simplifying 4(x + 3) * 3x = 7x + 12 Reorder the terms: 4(3 + x) * 3x = 7x + 12 Reorder the terms for easier multiplication: 4 * 3x(3 + x) = 7x + 12 Multiply 4 * 3 12x(3 + x) = 7x + 12 (3 * 12x + x * 12x) = 7x + 12 (36x + 12x2) = 7x + 12 Reorder the terms: 36x + 12x2 = 12 + 7x Solving 36x + 12x2 = 12 + 7x Solving for variable 'x'. Reorder the terms: -12 + 36x + -7x + 12x2 = 12 + 7x + -12 + -7x Combine like terms: 36x + -7x = 29x -12 + 29x + 12x2 = 12 + 7x + -12 + -7x Reorder the terms: -12 + 29x + 12x2 = 12 + -12 + 7x + -7x Combine like terms: 12 + -12 = 0 -12 + 29x + 12x2 = 0 + 7x + -7x -12 + 29x + 12x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -12 + 29x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1 + 2.416666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.416666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2.416666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.416666667x + x2 = 0 + 1 2.416666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.416666667x + x2 = 1 The x term is 2.416666667x. Take half its coefficient (1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. 2.416666667x + 1.460069446 + x2 = 1 + 1.460069446 Reorder the terms: 1.460069446 + 2.416666667x + x2 = 1 + 1.460069446 Combine like terms: 1 + 1.460069446 = 2.460069446 1.460069446 + 2.416666667x + x2 = 2.460069446 Factor a perfect square on the left side: (x + 1.208333334)(x + 1.208333334) = 2.460069446 Calculate the square root of the right side: 1.568460853 Break this problem into two subproblems by setting (x + 1.208333334) equal to 1.568460853 and -1.568460853.Subproblem 1
x + 1.208333334 = 1.568460853 Simplifying x + 1.208333334 = 1.568460853 Reorder the terms: 1.208333334 + x = 1.568460853 Solving 1.208333334 + x = 1.568460853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = 1.568460853 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = 1.568460853 + -1.208333334 x = 1.568460853 + -1.208333334 Combine like terms: 1.568460853 + -1.208333334 = 0.360127519 x = 0.360127519 Simplifying x = 0.360127519Subproblem 2
x + 1.208333334 = -1.568460853 Simplifying x + 1.208333334 = -1.568460853 Reorder the terms: 1.208333334 + x = -1.568460853 Solving 1.208333334 + x = -1.568460853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.208333334' to each side of the equation. 1.208333334 + -1.208333334 + x = -1.568460853 + -1.208333334 Combine like terms: 1.208333334 + -1.208333334 = 0.000000000 0.000000000 + x = -1.568460853 + -1.208333334 x = -1.568460853 + -1.208333334 Combine like terms: -1.568460853 + -1.208333334 = -2.776794187 x = -2.776794187 Simplifying x = -2.776794187Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.360127519, -2.776794187}
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