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Simplifying x + 6 = 4x2 + 12x + 9 Reorder the terms: 6 + x = 4x2 + 12x + 9 Reorder the terms: 6 + x = 9 + 12x + 4x2 Solving 6 + x = 9 + 12x + 4x2 Solving for variable 'x'. Reorder the terms: 6 + -9 + x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: 6 + -9 = -3 -3 + x + -12x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Combine like terms: x + -12x = -11x -3 + -11x + -4x2 = 9 + 12x + 4x2 + -9 + -12x + -4x2 Reorder the terms: -3 + -11x + -4x2 = 9 + -9 + 12x + -12x + 4x2 + -4x2 Combine like terms: 9 + -9 = 0 -3 + -11x + -4x2 = 0 + 12x + -12x + 4x2 + -4x2 -3 + -11x + -4x2 = 12x + -12x + 4x2 + -4x2 Combine like terms: 12x + -12x = 0 -3 + -11x + -4x2 = 0 + 4x2 + -4x2 -3 + -11x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + -11x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 11x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 11x + 4x2)' equal to zero and attempt to solve: Simplifying 3 + 11x + 4x2 = 0 Solving 3 + 11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 2.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2.75x + x2 = 0 + -0.75 2.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2.75x + x2 = -0.75 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = -0.75 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = -0.75 + 1.890625 Combine like terms: -0.75 + 1.890625 = 1.140625 1.890625 + 2.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 1.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 1.375 = 1.068000468 Simplifying x + 1.375 = 1.068000468 Reorder the terms: 1.375 + x = 1.068000468 Solving 1.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 1.068000468 + -1.375 x = 1.068000468 + -1.375 Combine like terms: 1.068000468 + -1.375 = -0.306999532 x = -0.306999532 Simplifying x = -0.306999532Subproblem 2
x + 1.375 = -1.068000468 Simplifying x + 1.375 = -1.068000468 Reorder the terms: 1.375 + x = -1.068000468 Solving 1.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -1.068000468 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -1.068000468 + -1.375 x = -1.068000468 + -1.375 Combine like terms: -1.068000468 + -1.375 = -2.443000468 x = -2.443000468 Simplifying x = -2.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.306999532, -2.443000468}Solution
x = {-0.306999532, -2.443000468}
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