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Simplifying 5x2 + 13x + 2 = 0 Reorder the terms: 2 + 13x + 5x2 = 0 Solving 2 + 13x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2.6x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2.6x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2.6x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2.6x + x2 = 0 + -0.4 2.6x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2.6x + x2 = -0.4 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 = -0.4 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = -0.4 + 1.69 Combine like terms: -0.4 + 1.69 = 1.29 1.69 + 2.6x + x2 = 1.29 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (x + 1.3) equal to 1.135781669 and -1.135781669.Subproblem 1
x + 1.3 = 1.135781669 Simplifying x + 1.3 = 1.135781669 Reorder the terms: 1.3 + x = 1.135781669 Solving 1.3 + x = 1.135781669 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 = 1.135781669 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 1.135781669 + -1.3 x = 1.135781669 + -1.3 Combine like terms: 1.135781669 + -1.3 = -0.164218331 x = -0.164218331 Simplifying x = -0.164218331Subproblem 2
x + 1.3 = -1.135781669 Simplifying x + 1.3 = -1.135781669 Reorder the terms: 1.3 + x = -1.135781669 Solving 1.3 + x = -1.135781669 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 = -1.135781669 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -1.135781669 + -1.3 x = -1.135781669 + -1.3 Combine like terms: -1.135781669 + -1.3 = -2.435781669 x = -2.435781669 Simplifying x = -2.435781669Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.164218331, -2.435781669}
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