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Simplifying 3(x + 4)(x + 4) = 21 Reorder the terms: 3(4 + x)(x + 4) = 21 Reorder the terms: 3(4 + x)(4 + x) = 21 Multiply (4 + x) * (4 + x) 3(4(4 + x) + x(4 + x)) = 21 3((4 * 4 + x * 4) + x(4 + x)) = 21 3((16 + 4x) + x(4 + x)) = 21 3(16 + 4x + (4 * x + x * x)) = 21 3(16 + 4x + (4x + x2)) = 21 Combine like terms: 4x + 4x = 8x 3(16 + 8x + x2) = 21 (16 * 3 + 8x * 3 + x2 * 3) = 21 (48 + 24x + 3x2) = 21 Solving 48 + 24x + 3x2 = 21 Solving for variable 'x'. Reorder the terms: 48 + -21 + 24x + 3x2 = 21 + -21 Combine like terms: 48 + -21 = 27 27 + 24x + 3x2 = 21 + -21 Combine like terms: 21 + -21 = 0 27 + 24x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(9 + 8x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(9 + 8x + x2)' equal to zero and attempt to solve: Simplifying 9 + 8x + x2 = 0 Solving 9 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 8x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x + x2 = 0 + -9 8x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 8x + x2 = -9 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -9 + 16 Reorder the terms: 16 + 8x + x2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8x + x2 = 7 Factor a perfect square on the left side: (x + 4)(x + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 4 = 2.645751311 Simplifying x + 4 = 2.645751311 Reorder the terms: 4 + x = 2.645751311 Solving 4 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.645751311 + -4 x = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 x = -1.354248689 Simplifying x = -1.354248689Subproblem 2
x + 4 = -2.645751311 Simplifying x + 4 = -2.645751311 Reorder the terms: 4 + x = -2.645751311 Solving 4 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.645751311 + -4 x = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 x = -6.645751311 Simplifying x = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.354248689, -6.645751311}Solution
x = {-1.354248689, -6.645751311}
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