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Simplifying 539 = 5x2 + 13x Reorder the terms: 539 = 13x + 5x2 Solving 539 = 13x + 5x2 Solving for variable 'x'. Reorder the terms: 539 + -13x + -5x2 = 13x + -13x + 5x2 + -5x2 Combine like terms: 13x + -13x = 0 539 + -13x + -5x2 = 0 + 5x2 + -5x2 539 + -13x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 539 + -13x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -107.8 + 2.6x + x2 = 0 Move the constant term to the right: Add '107.8' to each side of the equation. -107.8 + 2.6x + 107.8 + x2 = 0 + 107.8 Reorder the terms: -107.8 + 107.8 + 2.6x + x2 = 0 + 107.8 Combine like terms: -107.8 + 107.8 = 0.0 0.0 + 2.6x + x2 = 0 + 107.8 2.6x + x2 = 0 + 107.8 Combine like terms: 0 + 107.8 = 107.8 2.6x + x2 = 107.8 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 = 107.8 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 107.8 + 1.69 Combine like terms: 107.8 + 1.69 = 109.49 1.69 + 2.6x + x2 = 109.49 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 109.49 Calculate the square root of the right side: 10.463746939 Break this problem into two subproblems by setting (x + 1.3) equal to 10.463746939 and -10.463746939.Subproblem 1
x + 1.3 = 10.463746939 Simplifying x + 1.3 = 10.463746939 Reorder the terms: 1.3 + x = 10.463746939 Solving 1.3 + x = 10.463746939 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 = 10.463746939 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 10.463746939 + -1.3 x = 10.463746939 + -1.3 Combine like terms: 10.463746939 + -1.3 = 9.163746939 x = 9.163746939 Simplifying x = 9.163746939Subproblem 2
x + 1.3 = -10.463746939 Simplifying x + 1.3 = -10.463746939 Reorder the terms: 1.3 + x = -10.463746939 Solving 1.3 + x = -10.463746939 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 = -10.463746939 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -10.463746939 + -1.3 x = -10.463746939 + -1.3 Combine like terms: -10.463746939 + -1.3 = -11.763746939 x = -11.763746939 Simplifying x = -11.763746939Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.163746939, -11.763746939}
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