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Simplifying 19x2 + -13x = 12 Reorder the terms: -13x + 19x2 = 12 Solving -13x + 19x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -13x + 19x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -13x + 19x2 = 0 Begin completing the square. Divide all terms by 19 the coefficient of the squared term: Divide each side by '19'. -0.6315789474 + -0.6842105263x + x2 = 0 Move the constant term to the right: Add '0.6315789474' to each side of the equation. -0.6315789474 + -0.6842105263x + 0.6315789474 + x2 = 0 + 0.6315789474 Reorder the terms: -0.6315789474 + 0.6315789474 + -0.6842105263x + x2 = 0 + 0.6315789474 Combine like terms: -0.6315789474 + 0.6315789474 = 0.0000000000 0.0000000000 + -0.6842105263x + x2 = 0 + 0.6315789474 -0.6842105263x + x2 = 0 + 0.6315789474 Combine like terms: 0 + 0.6315789474 = 0.6315789474 -0.6842105263x + x2 = 0.6315789474 The x term is -0.6842105263x. Take half its coefficient (-0.3421052632). Square it (0.1170360111) and add it to both sides. Add '0.1170360111' to each side of the equation. -0.6842105263x + 0.1170360111 + x2 = 0.6315789474 + 0.1170360111 Reorder the terms: 0.1170360111 + -0.6842105263x + x2 = 0.6315789474 + 0.1170360111 Combine like terms: 0.6315789474 + 0.1170360111 = 0.7486149585 0.1170360111 + -0.6842105263x + x2 = 0.7486149585 Factor a perfect square on the left side: (x + -0.3421052632)(x + -0.3421052632) = 0.7486149585 Calculate the square root of the right side: 0.86522538 Break this problem into two subproblems by setting (x + -0.3421052632) equal to 0.86522538 and -0.86522538.Subproblem 1
x + -0.3421052632 = 0.86522538 Simplifying x + -0.3421052632 = 0.86522538 Reorder the terms: -0.3421052632 + x = 0.86522538 Solving -0.3421052632 + x = 0.86522538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = 0.86522538 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = 0.86522538 + 0.3421052632 x = 0.86522538 + 0.3421052632 Combine like terms: 0.86522538 + 0.3421052632 = 1.2073306432 x = 1.2073306432 Simplifying x = 1.2073306432Subproblem 2
x + -0.3421052632 = -0.86522538 Simplifying x + -0.3421052632 = -0.86522538 Reorder the terms: -0.3421052632 + x = -0.86522538 Solving -0.3421052632 + x = -0.86522538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3421052632' to each side of the equation. -0.3421052632 + 0.3421052632 + x = -0.86522538 + 0.3421052632 Combine like terms: -0.3421052632 + 0.3421052632 = 0.0000000000 0.0000000000 + x = -0.86522538 + 0.3421052632 x = -0.86522538 + 0.3421052632 Combine like terms: -0.86522538 + 0.3421052632 = -0.5231201168 x = -0.5231201168 Simplifying x = -0.5231201168Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2073306432, -0.5231201168}
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