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Simplifying (x + 3)(x + 4) = (10)(4) Reorder the terms: (3 + x)(x + 4) = (10)(4) Reorder the terms: (3 + x)(4 + x) = (10)(4) Multiply (3 + x) * (4 + x) (3(4 + x) + x(4 + x)) = (10)(4) ((4 * 3 + x * 3) + x(4 + x)) = (10)(4) ((12 + 3x) + x(4 + x)) = (10)(4) (12 + 3x + (4 * x + x * x)) = (10)(4) (12 + 3x + (4x + x2)) = (10)(4) Combine like terms: 3x + 4x = 7x (12 + 7x + x2) = (10)(4) Multiply 10 * 4 12 + 7x + x2 = 40 Solving 12 + 7x + x2 = 40 Solving for variable 'x'. Reorder the terms: 12 + -40 + 7x + x2 = 40 + -40 Combine like terms: 12 + -40 = -28 -28 + 7x + x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -28 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 7x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 7x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 7x + x2 = 0 + 28 7x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 7x + x2 = 28 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 28 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 28 + 12.25 Combine like terms: 28 + 12.25 = 40.25 12.25 + 7x + x2 = 40.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (x + 3.5) equal to 6.34428877 and -6.34428877.Subproblem 1
x + 3.5 = 6.34428877 Simplifying x + 3.5 = 6.34428877 Reorder the terms: 3.5 + x = 6.34428877 Solving 3.5 + x = 6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.34428877 + -3.5 x = 6.34428877 + -3.5 Combine like terms: 6.34428877 + -3.5 = 2.84428877 x = 2.84428877 Simplifying x = 2.84428877Subproblem 2
x + 3.5 = -6.34428877 Simplifying x + 3.5 = -6.34428877 Reorder the terms: 3.5 + x = -6.34428877 Solving 3.5 + x = -6.34428877 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -6.34428877 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.34428877 + -3.5 x = -6.34428877 + -3.5 Combine like terms: -6.34428877 + -3.5 = -9.84428877 x = -9.84428877 Simplifying x = -9.84428877Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.84428877, -9.84428877}
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