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Simplifying (x + 4)(x + 4) = 12(12 + x) Reorder the terms: (4 + x)(x + 4) = 12(12 + x) Reorder the terms: (4 + x)(4 + x) = 12(12 + x) Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) = 12(12 + x) ((4 * 4 + x * 4) + x(4 + x)) = 12(12 + x) ((16 + 4x) + x(4 + x)) = 12(12 + x) (16 + 4x + (4 * x + x * x)) = 12(12 + x) (16 + 4x + (4x + x2)) = 12(12 + x) Combine like terms: 4x + 4x = 8x (16 + 8x + x2) = 12(12 + x) 16 + 8x + x2 = (12 * 12 + x * 12) 16 + 8x + x2 = (144 + 12x) Solving 16 + 8x + x2 = 144 + 12x Solving for variable 'x'. Reorder the terms: 16 + -144 + 8x + -12x + x2 = 144 + 12x + -144 + -12x Combine like terms: 16 + -144 = -128 -128 + 8x + -12x + x2 = 144 + 12x + -144 + -12x Combine like terms: 8x + -12x = -4x -128 + -4x + x2 = 144 + 12x + -144 + -12x Reorder the terms: -128 + -4x + x2 = 144 + -144 + 12x + -12x Combine like terms: 144 + -144 = 0 -128 + -4x + x2 = 0 + 12x + -12x -128 + -4x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -128 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + -4x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + -4x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -4x + x2 = 0 + 128 -4x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 -4x + x2 = 128 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 128 + 4 Reorder the terms: 4 + -4x + x2 = 128 + 4 Combine like terms: 128 + 4 = 132 4 + -4x + x2 = 132 Factor a perfect square on the left side: (x + -2)(x + -2) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -2) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -2 = 11.489125293 Simplifying x + -2 = 11.489125293 Reorder the terms: -2 + x = 11.489125293 Solving -2 + x = 11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 11.489125293 + 2 Combine like terms: -2 + 2 = 0 0 + x = 11.489125293 + 2 x = 11.489125293 + 2 Combine like terms: 11.489125293 + 2 = 13.489125293 x = 13.489125293 Simplifying x = 13.489125293Subproblem 2
x + -2 = -11.489125293 Simplifying x + -2 = -11.489125293 Reorder the terms: -2 + x = -11.489125293 Solving -2 + x = -11.489125293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -11.489125293 + 2 Combine like terms: -2 + 2 = 0 0 + x = -11.489125293 + 2 x = -11.489125293 + 2 Combine like terms: -11.489125293 + 2 = -9.489125293 x = -9.489125293 Simplifying x = -9.489125293Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.489125293, -9.489125293}
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