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Simplifying x(5x + 13) = 16 Reorder the terms: x(13 + 5x) = 16 (13 * x + 5x * x) = 16 (13x + 5x2) = 16 Solving 13x + 5x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + 13x + 5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + 13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.2 + 2.6x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 2.6x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 2.6x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 2.6x + x2 = 0 + 3.2 2.6x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 2.6x + x2 = 3.2 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 3.2 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 3.2 + 1.69 Combine like terms: 3.2 + 1.69 = 4.89 1.69 + 2.6x + x2 = 4.89 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (x + 1.3) equal to 2.211334439 and -2.211334439.Subproblem 1
x + 1.3 = 2.211334439 Simplifying x + 1.3 = 2.211334439 Reorder the terms: 1.3 + x = 2.211334439 Solving 1.3 + x = 2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.211334439 + -1.3 x = 2.211334439 + -1.3 Combine like terms: 2.211334439 + -1.3 = 0.911334439 x = 0.911334439 Simplifying x = 0.911334439Subproblem 2
x + 1.3 = -2.211334439 Simplifying x + 1.3 = -2.211334439 Reorder the terms: 1.3 + x = -2.211334439 Solving 1.3 + x = -2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.211334439 + -1.3 x = -2.211334439 + -1.3 Combine like terms: -2.211334439 + -1.3 = -3.511334439 x = -3.511334439 Simplifying x = -3.511334439Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.911334439, -3.511334439}
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