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Simplifying (x + 5)(x + 5) = 2x2 + 3x + 36 Reorder the terms: (5 + x)(x + 5) = 2x2 + 3x + 36 Reorder the terms: (5 + x)(5 + x) = 2x2 + 3x + 36 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 2x2 + 3x + 36 ((5 * 5 + x * 5) + x(5 + x)) = 2x2 + 3x + 36 ((25 + 5x) + x(5 + x)) = 2x2 + 3x + 36 (25 + 5x + (5 * x + x * x)) = 2x2 + 3x + 36 (25 + 5x + (5x + x2)) = 2x2 + 3x + 36 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 2x2 + 3x + 36 Reorder the terms: 25 + 10x + x2 = 36 + 3x + 2x2 Solving 25 + 10x + x2 = 36 + 3x + 2x2 Solving for variable 'x'. Reorder the terms: 25 + -36 + 10x + -3x + x2 + -2x2 = 36 + 3x + 2x2 + -36 + -3x + -2x2 Combine like terms: 25 + -36 = -11 -11 + 10x + -3x + x2 + -2x2 = 36 + 3x + 2x2 + -36 + -3x + -2x2 Combine like terms: 10x + -3x = 7x -11 + 7x + x2 + -2x2 = 36 + 3x + 2x2 + -36 + -3x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -11 + 7x + -1x2 = 36 + 3x + 2x2 + -36 + -3x + -2x2 Reorder the terms: -11 + 7x + -1x2 = 36 + -36 + 3x + -3x + 2x2 + -2x2 Combine like terms: 36 + -36 = 0 -11 + 7x + -1x2 = 0 + 3x + -3x + 2x2 + -2x2 -11 + 7x + -1x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 -11 + 7x + -1x2 = 0 + 2x2 + -2x2 -11 + 7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -11 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -7x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -7x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x + x2 = 0 + -11 -7x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7x + x2 = -11 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 = -11 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -11 + 12.25 Combine like terms: -11 + 12.25 = 1.25 12.25 + -7x + x2 = 1.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -3.5) equal to 1.118033989 and -1.118033989.Subproblem 1
x + -3.5 = 1.118033989 Simplifying x + -3.5 = 1.118033989 Reorder the terms: -3.5 + x = 1.118033989 Solving -3.5 + x = 1.118033989 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 = 1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.118033989 + 3.5 x = 1.118033989 + 3.5 Combine like terms: 1.118033989 + 3.5 = 4.618033989 x = 4.618033989 Simplifying x = 4.618033989Subproblem 2
x + -3.5 = -1.118033989 Simplifying x + -3.5 = -1.118033989 Reorder the terms: -3.5 + x = -1.118033989 Solving -3.5 + x = -1.118033989 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 = -1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.118033989 + 3.5 x = -1.118033989 + 3.5 Combine like terms: -1.118033989 + 3.5 = 2.381966011 x = 2.381966011 Simplifying x = 2.381966011Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.618033989, 2.381966011}
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