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Simplifying 2x(x + 8) = 20 + 15 Reorder the terms: 2x(8 + x) = 20 + 15 (8 * 2x + x * 2x) = 20 + 15 (16x + 2x2) = 20 + 15 Combine like terms: 20 + 15 = 35 16x + 2x2 = 35 Solving 16x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + 16x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + 8x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 8x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 8x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 8x + x2 = 0 + 17.5 8x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 8x + x2 = 17.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 17.5 + 16 Reorder the terms: 16 + 8x + x2 = 17.5 + 16 Combine like terms: 17.5 + 16 = 33.5 16 + 8x + x2 = 33.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 33.5 Calculate the square root of the right side: 5.787918451 Break this problem into two subproblems by setting (x + 4) equal to 5.787918451 and -5.787918451.Subproblem 1
x + 4 = 5.787918451 Simplifying x + 4 = 5.787918451 Reorder the terms: 4 + x = 5.787918451 Solving 4 + x = 5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 5.787918451 + -4 Combine like terms: 4 + -4 = 0 0 + x = 5.787918451 + -4 x = 5.787918451 + -4 Combine like terms: 5.787918451 + -4 = 1.787918451 x = 1.787918451 Simplifying x = 1.787918451Subproblem 2
x + 4 = -5.787918451 Simplifying x + 4 = -5.787918451 Reorder the terms: 4 + x = -5.787918451 Solving 4 + x = -5.787918451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -5.787918451 + -4 Combine like terms: 4 + -4 = 0 0 + x = -5.787918451 + -4 x = -5.787918451 + -4 Combine like terms: -5.787918451 + -4 = -9.787918451 x = -9.787918451 Simplifying x = -9.787918451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.787918451, -9.787918451}
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