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Simplifying 13x2 + 2x + -7 = 0 Reorder the terms: -7 + 2x + 13x2 = 0 Solving -7 + 2x + 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'. -0.5384615385 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '0.5384615385' to each side of the equation. -0.5384615385 + 0.1538461538x + 0.5384615385 + x2 = 0 + 0.5384615385 Reorder the terms: -0.5384615385 + 0.5384615385 + 0.1538461538x + x2 = 0 + 0.5384615385 Combine like terms: -0.5384615385 + 0.5384615385 = 0.0000000000 0.0000000000 + 0.1538461538x + x2 = 0 + 0.5384615385 0.1538461538x + x2 = 0 + 0.5384615385 Combine like terms: 0 + 0.5384615385 = 0.5384615385 0.1538461538x + x2 = 0.5384615385 The x term is 0.1538461538x. Take half its coefficient (0.0769230769). Square it (0.005917159760) and add it to both sides. Add '0.005917159760' to each side of the equation. 0.1538461538x + 0.005917159760 + x2 = 0.5384615385 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 0.5384615385 + 0.005917159760 Combine like terms: 0.5384615385 + 0.005917159760 = 0.54437869826 0.005917159760 + 0.1538461538x + x2 = 0.54437869826 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 0.54437869826 Calculate the square root of the right side: 0.737820234 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 0.737820234 and -0.737820234.Subproblem 1
x + 0.0769230769 = 0.737820234 Simplifying x + 0.0769230769 = 0.737820234 Reorder the terms: 0.0769230769 + x = 0.737820234 Solving 0.0769230769 + x = 0.737820234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = 0.737820234 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 0.737820234 + -0.0769230769 x = 0.737820234 + -0.0769230769 Combine like terms: 0.737820234 + -0.0769230769 = 0.6608971571 x = 0.6608971571 Simplifying x = 0.6608971571Subproblem 2
x + 0.0769230769 = -0.737820234 Simplifying x + 0.0769230769 = -0.737820234 Reorder the terms: 0.0769230769 + x = -0.737820234 Solving 0.0769230769 + x = -0.737820234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0769230769' to each side of the equation. 0.0769230769 + -0.0769230769 + x = -0.737820234 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -0.737820234 + -0.0769230769 x = -0.737820234 + -0.0769230769 Combine like terms: -0.737820234 + -0.0769230769 = -0.8147433109 x = -0.8147433109 Simplifying x = -0.8147433109Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6608971571, -0.8147433109}
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