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Simplifying 5x2 + 13x = 13 Reorder the terms: 13x + 5x2 = 13 Solving 13x + 5x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 13x + 5x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 13x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.6 + 2.6x + x2 = 0 Move the constant term to the right: Add '2.6' to each side of the equation. -2.6 + 2.6x + 2.6 + x2 = 0 + 2.6 Reorder the terms: -2.6 + 2.6 + 2.6x + x2 = 0 + 2.6 Combine like terms: -2.6 + 2.6 = 0.0 0.0 + 2.6x + x2 = 0 + 2.6 2.6x + x2 = 0 + 2.6 Combine like terms: 0 + 2.6 = 2.6 2.6x + x2 = 2.6 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 = 2.6 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 2.6 + 1.69 Combine like terms: 2.6 + 1.69 = 4.29 1.69 + 2.6x + x2 = 4.29 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 4.29 Calculate the square root of the right side: 2.071231518 Break this problem into two subproblems by setting (x + 1.3) equal to 2.071231518 and -2.071231518.Subproblem 1
x + 1.3 = 2.071231518 Simplifying x + 1.3 = 2.071231518 Reorder the terms: 1.3 + x = 2.071231518 Solving 1.3 + x = 2.071231518 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 = 2.071231518 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.071231518 + -1.3 x = 2.071231518 + -1.3 Combine like terms: 2.071231518 + -1.3 = 0.771231518 x = 0.771231518 Simplifying x = 0.771231518Subproblem 2
x + 1.3 = -2.071231518 Simplifying x + 1.3 = -2.071231518 Reorder the terms: 1.3 + x = -2.071231518 Solving 1.3 + x = -2.071231518 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 = -2.071231518 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.071231518 + -1.3 x = -2.071231518 + -1.3 Combine like terms: -2.071231518 + -1.3 = -3.371231518 x = -3.371231518 Simplifying x = -3.371231518Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.771231518, -3.371231518}
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