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Simplifying -13x2 + 500x + 140 = 0 Reorder the terms: 140 + 500x + -13x2 = 0 Solving 140 + 500x + -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'. -10.76923077 + -38.46153846x + x2 = 0 Move the constant term to the right: Add '10.76923077' to each side of the equation. -10.76923077 + -38.46153846x + 10.76923077 + x2 = 0 + 10.76923077 Reorder the terms: -10.76923077 + 10.76923077 + -38.46153846x + x2 = 0 + 10.76923077 Combine like terms: -10.76923077 + 10.76923077 = 0.00000000 0.00000000 + -38.46153846x + x2 = 0 + 10.76923077 -38.46153846x + x2 = 0 + 10.76923077 Combine like terms: 0 + 10.76923077 = 10.76923077 -38.46153846x + x2 = 10.76923077 The x term is -38.46153846x. Take half its coefficient (-19.23076923). Square it (369.8224852) and add it to both sides. Add '369.8224852' to each side of the equation. -38.46153846x + 369.8224852 + x2 = 10.76923077 + 369.8224852 Reorder the terms: 369.8224852 + -38.46153846x + x2 = 10.76923077 + 369.8224852 Combine like terms: 10.76923077 + 369.8224852 = 380.59171597 369.8224852 + -38.46153846x + x2 = 380.59171597 Factor a perfect square on the left side: (x + -19.23076923)(x + -19.23076923) = 380.59171597 Calculate the square root of the right side: 19.50875998 Break this problem into two subproblems by setting (x + -19.23076923) equal to 19.50875998 and -19.50875998.Subproblem 1
x + -19.23076923 = 19.50875998 Simplifying x + -19.23076923 = 19.50875998 Reorder the terms: -19.23076923 + x = 19.50875998 Solving -19.23076923 + x = 19.50875998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.23076923' to each side of the equation. -19.23076923 + 19.23076923 + x = 19.50875998 + 19.23076923 Combine like terms: -19.23076923 + 19.23076923 = 0.00000000 0.00000000 + x = 19.50875998 + 19.23076923 x = 19.50875998 + 19.23076923 Combine like terms: 19.50875998 + 19.23076923 = 38.73952921 x = 38.73952921 Simplifying x = 38.73952921Subproblem 2
x + -19.23076923 = -19.50875998 Simplifying x + -19.23076923 = -19.50875998 Reorder the terms: -19.23076923 + x = -19.50875998 Solving -19.23076923 + x = -19.50875998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.23076923' to each side of the equation. -19.23076923 + 19.23076923 + x = -19.50875998 + 19.23076923 Combine like terms: -19.23076923 + 19.23076923 = 0.00000000 0.00000000 + x = -19.50875998 + 19.23076923 x = -19.50875998 + 19.23076923 Combine like terms: -19.50875998 + 19.23076923 = -0.27799075 x = -0.27799075 Simplifying x = -0.27799075Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.73952921, -0.27799075}
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