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Simplifying 13x2 + -1x + -188 = 0 Reorder the terms: -188 + -1x + 13x2 = 0 Solving -188 + -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'. -14.46153846 + -0.07692307692x + x2 = 0 Move the constant term to the right: Add '14.46153846' to each side of the equation. -14.46153846 + -0.07692307692x + 14.46153846 + x2 = 0 + 14.46153846 Reorder the terms: -14.46153846 + 14.46153846 + -0.07692307692x + x2 = 0 + 14.46153846 Combine like terms: -14.46153846 + 14.46153846 = 0.00000000 0.00000000 + -0.07692307692x + x2 = 0 + 14.46153846 -0.07692307692x + x2 = 0 + 14.46153846 Combine like terms: 0 + 14.46153846 = 14.46153846 -0.07692307692x + x2 = 14.46153846 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 = 14.46153846 + 0.001479289941 Reorder the terms: 0.001479289941 + -0.07692307692x + x2 = 14.46153846 + 0.001479289941 Combine like terms: 14.46153846 + 0.001479289941 = 14.463017749941 0.001479289941 + -0.07692307692x + x2 = 14.463017749941 Factor a perfect square on the left side: (x + -0.03846153846)(x + -0.03846153846) = 14.463017749941 Calculate the square root of the right side: 3.803027445 Break this problem into two subproblems by setting (x + -0.03846153846) equal to 3.803027445 and -3.803027445.Subproblem 1
x + -0.03846153846 = 3.803027445 Simplifying x + -0.03846153846 = 3.803027445 Reorder the terms: -0.03846153846 + x = 3.803027445 Solving -0.03846153846 + x = 3.803027445 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 = 3.803027445 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = 3.803027445 + 0.03846153846 x = 3.803027445 + 0.03846153846 Combine like terms: 3.803027445 + 0.03846153846 = 3.84148898346 x = 3.84148898346 Simplifying x = 3.84148898346Subproblem 2
x + -0.03846153846 = -3.803027445 Simplifying x + -0.03846153846 = -3.803027445 Reorder the terms: -0.03846153846 + x = -3.803027445 Solving -0.03846153846 + x = -3.803027445 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 = -3.803027445 + 0.03846153846 Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000 0.00000000000 + x = -3.803027445 + 0.03846153846 x = -3.803027445 + 0.03846153846 Combine like terms: -3.803027445 + 0.03846153846 = -3.76456590654 x = -3.76456590654 Simplifying x = -3.76456590654Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.84148898346, -3.76456590654}
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