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Simplifying 36 = (x + 3)(x + 4) Reorder the terms: 36 = (3 + x)(x + 4) Reorder the terms: 36 = (3 + x)(4 + x) Multiply (3 + x) * (4 + x) 36 = (3(4 + x) + x(4 + x)) 36 = ((4 * 3 + x * 3) + x(4 + x)) 36 = ((12 + 3x) + x(4 + x)) 36 = (12 + 3x + (4 * x + x * x)) 36 = (12 + 3x + (4x + x2)) Combine like terms: 3x + 4x = 7x 36 = (12 + 7x + x2) Solving 36 = 12 + 7x + x2 Solving for variable 'x'. Combine like terms: 36 + -12 = 24 24 + -7x + -1x2 = 12 + 7x + x2 + -12 + -7x + -1x2 Reorder the terms: 24 + -7x + -1x2 = 12 + -12 + 7x + -7x + x2 + -1x2 Combine like terms: 12 + -12 = 0 24 + -7x + -1x2 = 0 + 7x + -7x + x2 + -1x2 24 + -7x + -1x2 = 7x + -7x + x2 + -1x2 Combine like terms: 7x + -7x = 0 24 + -7x + -1x2 = 0 + x2 + -1x2 24 + -7x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 24 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -24 + 7x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 7x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 7x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 7x + x2 = 0 + 24 7x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 7x + x2 = 24 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 = 24 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 24 + 12.25 Combine like terms: 24 + 12.25 = 36.25 12.25 + 7x + x2 = 36.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + 3.5) equal to 6.020797289 and -6.020797289.Subproblem 1
x + 3.5 = 6.020797289 Simplifying x + 3.5 = 6.020797289 Reorder the terms: 3.5 + x = 6.020797289 Solving 3.5 + x = 6.020797289 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 = 6.020797289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 6.020797289 + -3.5 x = 6.020797289 + -3.5 Combine like terms: 6.020797289 + -3.5 = 2.520797289 x = 2.520797289 Simplifying x = 2.520797289Subproblem 2
x + 3.5 = -6.020797289 Simplifying x + 3.5 = -6.020797289 Reorder the terms: 3.5 + x = -6.020797289 Solving 3.5 + x = -6.020797289 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 = -6.020797289 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -6.020797289 + -3.5 x = -6.020797289 + -3.5 Combine like terms: -6.020797289 + -3.5 = -9.520797289 x = -9.520797289 Simplifying x = -9.520797289Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.520797289, -9.520797289}
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