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Simplifying 13x2 + 26x + 4 = 0 Reorder the terms: 4 + 26x + 13x2 = 0 Solving 4 + 26x + 13x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.3076923077 + 2x + x2 = 0 Move the constant term to the right: Add '-0.3076923077' to each side of the equation. 0.3076923077 + 2x + -0.3076923077 + x2 = 0 + -0.3076923077 Reorder the terms: 0.3076923077 + -0.3076923077 + 2x + x2 = 0 + -0.3076923077 Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.3076923077 2x + x2 = 0 + -0.3076923077 Combine like terms: 0 + -0.3076923077 = -0.3076923077 2x + x2 = -0.3076923077 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.3076923077 + 1 Reorder the terms: 1 + 2x + x2 = -0.3076923077 + 1 Combine like terms: -0.3076923077 + 1 = 0.6923076923 1 + 2x + x2 = 0.6923076923 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.6923076923 Calculate the square root of the right side: 0.832050294 Break this problem into two subproblems by setting (x + 1) equal to 0.832050294 and -0.832050294.Subproblem 1
x + 1 = 0.832050294 Simplifying x + 1 = 0.832050294 Reorder the terms: 1 + x = 0.832050294 Solving 1 + x = 0.832050294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.832050294 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.832050294 + -1 x = 0.832050294 + -1 Combine like terms: 0.832050294 + -1 = -0.167949706 x = -0.167949706 Simplifying x = -0.167949706Subproblem 2
x + 1 = -0.832050294 Simplifying x + 1 = -0.832050294 Reorder the terms: 1 + x = -0.832050294 Solving 1 + x = -0.832050294 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.832050294 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.832050294 + -1 x = -0.832050294 + -1 Combine like terms: -0.832050294 + -1 = -1.832050294 x = -1.832050294 Simplifying x = -1.832050294Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.167949706, -1.832050294}
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