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Simplifying 4x(x + 6) = 56 Reorder the terms: 4x(6 + x) = 56 (6 * 4x + x * 4x) = 56 (24x + 4x2) = 56 Solving 24x + 4x2 = 56 Solving for variable 'x'. Reorder the terms: -56 + 24x + 4x2 = 56 + -56 Combine like terms: 56 + -56 = 0 -56 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-14 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-14 + 6x + x2)' equal to zero and attempt to solve: Simplifying -14 + 6x + x2 = 0 Solving -14 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 6x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + 6x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 6x + x2 = 0 + 14 6x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 6x + x2 = 14 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 = 14 + 9 Reorder the terms: 9 + 6x + x2 = 14 + 9 Combine like terms: 14 + 9 = 23 9 + 6x + x2 = 23 Factor a perfect square on the left side: (x + 3)(x + 3) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 3) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 3 = 4.795831523 Simplifying x + 3 = 4.795831523 Reorder the terms: 3 + x = 4.795831523 Solving 3 + x = 4.795831523 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 = 4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.795831523 + -3 x = 4.795831523 + -3 Combine like terms: 4.795831523 + -3 = 1.795831523 x = 1.795831523 Simplifying x = 1.795831523Subproblem 2
x + 3 = -4.795831523 Simplifying x + 3 = -4.795831523 Reorder the terms: 3 + x = -4.795831523 Solving 3 + x = -4.795831523 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 = -4.795831523 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.795831523 + -3 x = -4.795831523 + -3 Combine like terms: -4.795831523 + -3 = -7.795831523 x = -7.795831523 Simplifying x = -7.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.795831523, -7.795831523}Solution
x = {1.795831523, -7.795831523}
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