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Simplifying 2x(5x + 15) = 27 Reorder the terms: 2x(15 + 5x) = 27 (15 * 2x + 5x * 2x) = 27 (30x + 10x2) = 27 Solving 30x + 10x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 30x + 10x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 30x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.7 + 3x + x2 = 0.0 Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + 3x + 2.7 + x2 = 0.0 + 2.7 Reorder the terms: -2.7 + 2.7 + 3x + x2 = 0.0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + 3x + x2 = 0.0 + 2.7 3x + x2 = 0.0 + 2.7 Combine like terms: 0.0 + 2.7 = 2.7 3x + x2 = 2.7 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2.7 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.7 + 2.25 Combine like terms: 2.7 + 2.25 = 4.95 2.25 + 3x + x2 = 4.95 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.95 Calculate the square root of the right side: 2.224859546 Break this problem into two subproblems by setting (x + 1.5) equal to 2.224859546 and -2.224859546.Subproblem 1
x + 1.5 = 2.224859546 Simplifying x + 1.5 = 2.224859546 Reorder the terms: 1.5 + x = 2.224859546 Solving 1.5 + x = 2.224859546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.224859546 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.224859546 + -1.5 x = 2.224859546 + -1.5 Combine like terms: 2.224859546 + -1.5 = 0.724859546 x = 0.724859546 Simplifying x = 0.724859546Subproblem 2
x + 1.5 = -2.224859546 Simplifying x + 1.5 = -2.224859546 Reorder the terms: 1.5 + x = -2.224859546 Solving 1.5 + x = -2.224859546 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.224859546 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.224859546 + -1.5 x = -2.224859546 + -1.5 Combine like terms: -2.224859546 + -1.5 = -3.724859546 x = -3.724859546 Simplifying x = -3.724859546Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.724859546, -3.724859546}
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