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Simplifying 13x2 + 36x + -32 = 0 Reorder the terms: -32 + 36x + 13x2 = 0 Solving -32 + 36x + 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'. -2.461538462 + 2.769230769x + x2 = 0 Move the constant term to the right: Add '2.461538462' to each side of the equation. -2.461538462 + 2.769230769x + 2.461538462 + x2 = 0 + 2.461538462 Reorder the terms: -2.461538462 + 2.461538462 + 2.769230769x + x2 = 0 + 2.461538462 Combine like terms: -2.461538462 + 2.461538462 = 0.000000000 0.000000000 + 2.769230769x + x2 = 0 + 2.461538462 2.769230769x + x2 = 0 + 2.461538462 Combine like terms: 0 + 2.461538462 = 2.461538462 2.769230769x + x2 = 2.461538462 The x term is 2.769230769x. Take half its coefficient (1.384615385). Square it (1.917159764) and add it to both sides. Add '1.917159764' to each side of the equation. 2.769230769x + 1.917159764 + x2 = 2.461538462 + 1.917159764 Reorder the terms: 1.917159764 + 2.769230769x + x2 = 2.461538462 + 1.917159764 Combine like terms: 2.461538462 + 1.917159764 = 4.378698226 1.917159764 + 2.769230769x + x2 = 4.378698226 Factor a perfect square on the left side: (x + 1.384615385)(x + 1.384615385) = 4.378698226 Calculate the square root of the right side: 2.092533925 Break this problem into two subproblems by setting (x + 1.384615385) equal to 2.092533925 and -2.092533925.Subproblem 1
x + 1.384615385 = 2.092533925 Simplifying x + 1.384615385 = 2.092533925 Reorder the terms: 1.384615385 + x = 2.092533925 Solving 1.384615385 + x = 2.092533925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.384615385' to each side of the equation. 1.384615385 + -1.384615385 + x = 2.092533925 + -1.384615385 Combine like terms: 1.384615385 + -1.384615385 = 0.000000000 0.000000000 + x = 2.092533925 + -1.384615385 x = 2.092533925 + -1.384615385 Combine like terms: 2.092533925 + -1.384615385 = 0.70791854 x = 0.70791854 Simplifying x = 0.70791854Subproblem 2
x + 1.384615385 = -2.092533925 Simplifying x + 1.384615385 = -2.092533925 Reorder the terms: 1.384615385 + x = -2.092533925 Solving 1.384615385 + x = -2.092533925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.384615385' to each side of the equation. 1.384615385 + -1.384615385 + x = -2.092533925 + -1.384615385 Combine like terms: 1.384615385 + -1.384615385 = 0.000000000 0.000000000 + x = -2.092533925 + -1.384615385 x = -2.092533925 + -1.384615385 Combine like terms: -2.092533925 + -1.384615385 = -3.47714931 x = -3.47714931 Simplifying x = -3.47714931Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.70791854, -3.47714931}
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