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Simplifying 3x(4x + 6) = 9x + 12 Reorder the terms: 3x(6 + 4x) = 9x + 12 (6 * 3x + 4x * 3x) = 9x + 12 (18x + 12x2) = 9x + 12 Reorder the terms: 18x + 12x2 = 12 + 9x Solving 18x + 12x2 = 12 + 9x Solving for variable 'x'. Reorder the terms: -12 + 18x + -9x + 12x2 = 12 + 9x + -12 + -9x Combine like terms: 18x + -9x = 9x -12 + 9x + 12x2 = 12 + 9x + -12 + -9x Reorder the terms: -12 + 9x + 12x2 = 12 + -12 + 9x + -9x Combine like terms: 12 + -12 = 0 -12 + 9x + 12x2 = 0 + 9x + -9x -12 + 9x + 12x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -12 + 9x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 3x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 4x2 = 0 Solving -4 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 0.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.75x + x2 = 0 + 1 0.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.75x + x2 = 1 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + 0.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 0.375 = 1.068000468 Simplifying x + 0.375 = 1.068000468 Reorder the terms: 0.375 + x = 1.068000468 Solving 0.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.068000468 + -0.375 x = 1.068000468 + -0.375 Combine like terms: 1.068000468 + -0.375 = 0.693000468 x = 0.693000468 Simplifying x = 0.693000468Subproblem 2
x + 0.375 = -1.068000468 Simplifying x + 0.375 = -1.068000468 Reorder the terms: 0.375 + x = -1.068000468 Solving 0.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.068000468 + -0.375 x = -1.068000468 + -0.375 Combine like terms: -1.068000468 + -0.375 = -1.443000468 x = -1.443000468 Simplifying x = -1.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.693000468, -1.443000468}Solution
x = {0.693000468, -1.443000468}
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