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Simplifying 13x2 + 19x + -3 = 0 Reorder the terms: -3 + 19x + 13x2 = 0 Solving -3 + 19x + 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'. -0.2307692308 + 1.461538462x + x2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + 1.461538462x + 0.2307692308 + x2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + 1.461538462x + x2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + 1.461538462x + x2 = 0 + 0.2307692308 1.461538462x + x2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 1.461538462x + x2 = 0.2307692308 The x term is 1.461538462x. Take half its coefficient (0.730769231). Square it (0.5340236690) and add it to both sides. Add '0.5340236690' to each side of the equation. 1.461538462x + 0.5340236690 + x2 = 0.2307692308 + 0.5340236690 Reorder the terms: 0.5340236690 + 1.461538462x + x2 = 0.2307692308 + 0.5340236690 Combine like terms: 0.2307692308 + 0.5340236690 = 0.7647928998 0.5340236690 + 1.461538462x + x2 = 0.7647928998 Factor a perfect square on the left side: (x + 0.730769231)(x + 0.730769231) = 0.7647928998 Calculate the square root of the right side: 0.874524385 Break this problem into two subproblems by setting (x + 0.730769231) equal to 0.874524385 and -0.874524385.Subproblem 1
x + 0.730769231 = 0.874524385 Simplifying x + 0.730769231 = 0.874524385 Reorder the terms: 0.730769231 + x = 0.874524385 Solving 0.730769231 + x = 0.874524385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.730769231' to each side of the equation. 0.730769231 + -0.730769231 + x = 0.874524385 + -0.730769231 Combine like terms: 0.730769231 + -0.730769231 = 0.000000000 0.000000000 + x = 0.874524385 + -0.730769231 x = 0.874524385 + -0.730769231 Combine like terms: 0.874524385 + -0.730769231 = 0.143755154 x = 0.143755154 Simplifying x = 0.143755154Subproblem 2
x + 0.730769231 = -0.874524385 Simplifying x + 0.730769231 = -0.874524385 Reorder the terms: 0.730769231 + x = -0.874524385 Solving 0.730769231 + x = -0.874524385 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.730769231' to each side of the equation. 0.730769231 + -0.730769231 + x = -0.874524385 + -0.730769231 Combine like terms: 0.730769231 + -0.730769231 = 0.000000000 0.000000000 + x = -0.874524385 + -0.730769231 x = -0.874524385 + -0.730769231 Combine like terms: -0.874524385 + -0.730769231 = -1.605293616 x = -1.605293616 Simplifying x = -1.605293616Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143755154, -1.605293616}
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