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Simplifying 226.6 = (15 + 2x)(11 + 2x) Multiply (15 + 2x) * (11 + 2x) 226.6 = (15(11 + 2x) + 2x * (11 + 2x)) 226.6 = ((11 * 15 + 2x * 15) + 2x * (11 + 2x)) 226.6 = ((165 + 30x) + 2x * (11 + 2x)) 226.6 = (165 + 30x + (11 * 2x + 2x * 2x)) 226.6 = (165 + 30x + (22x + 4x2)) Combine like terms: 30x + 22x = 52x 226.6 = (165 + 52x + 4x2) Solving 226.6 = 165 + 52x + 4x2 Solving for variable 'x'. Combine like terms: 226.6 + -165 = 61.6 61.6 + -52x + -4x2 = 165 + 52x + 4x2 + -165 + -52x + -4x2 Reorder the terms: 61.6 + -52x + -4x2 = 165 + -165 + 52x + -52x + 4x2 + -4x2 Combine like terms: 165 + -165 = 0 61.6 + -52x + -4x2 = 0 + 52x + -52x + 4x2 + -4x2 61.6 + -52x + -4x2 = 52x + -52x + 4x2 + -4x2 Combine like terms: 52x + -52x = 0 61.6 + -52x + -4x2 = 0 + 4x2 + -4x2 61.6 + -52x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 61.6 + -52x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -15.4 + 13x + x2 = 0 Move the constant term to the right: Add '15.4' to each side of the equation. -15.4 + 13x + 15.4 + x2 = 0 + 15.4 Reorder the terms: -15.4 + 15.4 + 13x + x2 = 0 + 15.4 Combine like terms: -15.4 + 15.4 = 0.0 0.0 + 13x + x2 = 0 + 15.4 13x + x2 = 0 + 15.4 Combine like terms: 0 + 15.4 = 15.4 13x + x2 = 15.4 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 15.4 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 15.4 + 42.25 Combine like terms: 15.4 + 42.25 = 57.65 42.25 + 13x + x2 = 57.65 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 57.65 Calculate the square root of the right side: 7.592759709 Break this problem into two subproblems by setting (x + 6.5) equal to 7.592759709 and -7.592759709.Subproblem 1
x + 6.5 = 7.592759709 Simplifying x + 6.5 = 7.592759709 Reorder the terms: 6.5 + x = 7.592759709 Solving 6.5 + x = 7.592759709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.592759709 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.592759709 + -6.5 x = 7.592759709 + -6.5 Combine like terms: 7.592759709 + -6.5 = 1.092759709 x = 1.092759709 Simplifying x = 1.092759709Subproblem 2
x + 6.5 = -7.592759709 Simplifying x + 6.5 = -7.592759709 Reorder the terms: 6.5 + x = -7.592759709 Solving 6.5 + x = -7.592759709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.592759709 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.592759709 + -6.5 x = -7.592759709 + -6.5 Combine like terms: -7.592759709 + -6.5 = -14.092759709 x = -14.092759709 Simplifying x = -14.092759709Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.092759709, -14.092759709}
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