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Simplifying 215 = (5 + x)(4 + 2x) Multiply (5 + x) * (4 + 2x) 215 = (5(4 + 2x) + x(4 + 2x)) 215 = ((4 * 5 + 2x * 5) + x(4 + 2x)) 215 = ((20 + 10x) + x(4 + 2x)) 215 = (20 + 10x + (4 * x + 2x * x)) 215 = (20 + 10x + (4x + 2x2)) Combine like terms: 10x + 4x = 14x 215 = (20 + 14x + 2x2) Solving 215 = 20 + 14x + 2x2 Solving for variable 'x'. Combine like terms: 215 + -20 = 195 195 + -14x + -2x2 = 20 + 14x + 2x2 + -20 + -14x + -2x2 Reorder the terms: 195 + -14x + -2x2 = 20 + -20 + 14x + -14x + 2x2 + -2x2 Combine like terms: 20 + -20 = 0 195 + -14x + -2x2 = 0 + 14x + -14x + 2x2 + -2x2 195 + -14x + -2x2 = 14x + -14x + 2x2 + -2x2 Combine like terms: 14x + -14x = 0 195 + -14x + -2x2 = 0 + 2x2 + -2x2 195 + -14x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 195 + -14x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -97.5 + 7x + x2 = 0 Move the constant term to the right: Add '97.5' to each side of the equation. -97.5 + 7x + 97.5 + x2 = 0 + 97.5 Reorder the terms: -97.5 + 97.5 + 7x + x2 = 0 + 97.5 Combine like terms: -97.5 + 97.5 = 0.0 0.0 + 7x + x2 = 0 + 97.5 7x + x2 = 0 + 97.5 Combine like terms: 0 + 97.5 = 97.5 7x + x2 = 97.5 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 = 97.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 97.5 + 12.25 Combine like terms: 97.5 + 12.25 = 109.75 12.25 + 7x + x2 = 109.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 109.75 Calculate the square root of the right side: 10.47616342 Break this problem into two subproblems by setting (x + 3.5) equal to 10.47616342 and -10.47616342.Subproblem 1
x + 3.5 = 10.47616342 Simplifying x + 3.5 = 10.47616342 Reorder the terms: 3.5 + x = 10.47616342 Solving 3.5 + x = 10.47616342 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 = 10.47616342 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 10.47616342 + -3.5 x = 10.47616342 + -3.5 Combine like terms: 10.47616342 + -3.5 = 6.97616342 x = 6.97616342 Simplifying x = 6.97616342Subproblem 2
x + 3.5 = -10.47616342 Simplifying x + 3.5 = -10.47616342 Reorder the terms: 3.5 + x = -10.47616342 Solving 3.5 + x = -10.47616342 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 = -10.47616342 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -10.47616342 + -3.5 x = -10.47616342 + -3.5 Combine like terms: -10.47616342 + -3.5 = -13.97616342 x = -13.97616342 Simplifying x = -13.97616342Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.97616342, -13.97616342}
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