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Simplifying 13x2 + 2x + 2 = 134 Reorder the terms: 2 + 2x + 13x2 = 134 Solving 2 + 2x + 13x2 = 134 Solving for variable 'x'. Reorder the terms: 2 + -134 + 2x + 13x2 = 134 + -134 Combine like terms: 2 + -134 = -132 -132 + 2x + 13x2 = 134 + -134 Combine like terms: 134 + -134 = 0 -132 + 2x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -10.15384615 + 0.1538461538x + x2 = 0 Move the constant term to the right: Add '10.15384615' to each side of the equation. -10.15384615 + 0.1538461538x + 10.15384615 + x2 = 0 + 10.15384615 Reorder the terms: -10.15384615 + 10.15384615 + 0.1538461538x + x2 = 0 + 10.15384615 Combine like terms: -10.15384615 + 10.15384615 = 0.00000000 0.00000000 + 0.1538461538x + x2 = 0 + 10.15384615 0.1538461538x + x2 = 0 + 10.15384615 Combine like terms: 0 + 10.15384615 = 10.15384615 0.1538461538x + x2 = 10.15384615 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 = 10.15384615 + 0.005917159760 Reorder the terms: 0.005917159760 + 0.1538461538x + x2 = 10.15384615 + 0.005917159760 Combine like terms: 10.15384615 + 0.005917159760 = 10.15976330976 0.005917159760 + 0.1538461538x + x2 = 10.15976330976 Factor a perfect square on the left side: (x + 0.0769230769)(x + 0.0769230769) = 10.15976330976 Calculate the square root of the right side: 3.187438362 Break this problem into two subproblems by setting (x + 0.0769230769) equal to 3.187438362 and -3.187438362.Subproblem 1
x + 0.0769230769 = 3.187438362 Simplifying x + 0.0769230769 = 3.187438362 Reorder the terms: 0.0769230769 + x = 3.187438362 Solving 0.0769230769 + x = 3.187438362 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 = 3.187438362 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = 3.187438362 + -0.0769230769 x = 3.187438362 + -0.0769230769 Combine like terms: 3.187438362 + -0.0769230769 = 3.1105152851 x = 3.1105152851 Simplifying x = 3.1105152851Subproblem 2
x + 0.0769230769 = -3.187438362 Simplifying x + 0.0769230769 = -3.187438362 Reorder the terms: 0.0769230769 + x = -3.187438362 Solving 0.0769230769 + x = -3.187438362 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 = -3.187438362 + -0.0769230769 Combine like terms: 0.0769230769 + -0.0769230769 = 0.0000000000 0.0000000000 + x = -3.187438362 + -0.0769230769 x = -3.187438362 + -0.0769230769 Combine like terms: -3.187438362 + -0.0769230769 = -3.2643614389 x = -3.2643614389 Simplifying x = -3.2643614389Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1105152851, -3.2643614389}
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