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Simplifying 13x2 + -1x + -3 = 0 Reorder the terms: -3 + -1x + 13x2 = 0 Solving -3 + -1x + 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 + -0.07692307692x + x2 = 0 Move the constant term to the right: Add '0.2307692308' to each side of the equation. -0.2307692308 + -0.07692307692x + 0.2307692308 + x2 = 0 + 0.2307692308 Reorder the terms: -0.2307692308 + 0.2307692308 + -0.07692307692x + x2 = 0 + 0.2307692308 Combine like terms: -0.2307692308 + 0.2307692308 = 0.0000000000 0.0000000000 + -0.07692307692x + x2 = 0 + 0.2307692308 -0.07692307692x + x2 = 0 + 0.2307692308 Combine like terms: 0 + 0.2307692308 = 0.2307692308 -0.07692307692x + x2 = 0.2307692308 The x term is -0.07692307692x. Take half its coefficient (-0.03846153846). Square it (0.001479289941) and add it to both sides. Add '0.001479289941' to each side of the equation. -0.07692307692x + 0.001479289941 + x2 = 0.2307692308 + 0.001479289941 Reorder the terms: 0.001479289941 + -0.07692307692x + x2 = 0.2307692308 + 0.001479289941 Combine like terms: 0.2307692308 + 0.001479289941 = 0.232248520741 0.001479289941 + -0.07692307692x + x2 = 0.232248520741 Factor a perfect square on the left side: (x + -0.03846153846)(x + -0.03846153846) = 0.232248520741 Calculate the square root of the right side: 0.481921696 Break this problem into two subproblems by setting (x + -0.03846153846) equal to 0.481921696 and -0.481921696.Subproblem 1
x + -0.03846153846 = 0.481921696 Simplifying x + -0.03846153846 = 0.481921696 Reorder the terms: -0.03846153846 + x = 0.481921696 Solving -0.03846153846 + x = 0.481921696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + x = 0.481921696 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = 0.481921696 + 0.03846153846 x = 0.481921696 + 0.03846153846 Combine like terms: 0.481921696 + 0.03846153846 = 0.52038323446 x = 0.52038323446 Simplifying x = 0.52038323446Subproblem 2
x + -0.03846153846 = -0.481921696 Simplifying x + -0.03846153846 = -0.481921696 Reorder the terms: -0.03846153846 + x = -0.481921696 Solving -0.03846153846 + x = -0.481921696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03846153846' to each side of the equation. -0.03846153846 + 0.03846153846 + x = -0.481921696 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = -0.481921696 + 0.03846153846 x = -0.481921696 + 0.03846153846 Combine like terms: -0.481921696 + 0.03846153846 = -0.44346015754 x = -0.44346015754 Simplifying x = -0.44346015754Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.52038323446, -0.44346015754}
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