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Simplifying 99x2 + -695x + -500 = 0 Reorder the terms: -500 + -695x + 99x2 = 0 Solving -500 + -695x + 99x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 99 the coefficient of the squared term: Divide each side by '99'. -5.050505051 + -7.02020202x + x2 = 0 Move the constant term to the right: Add '5.050505051' to each side of the equation. -5.050505051 + -7.02020202x + 5.050505051 + x2 = 0 + 5.050505051 Reorder the terms: -5.050505051 + 5.050505051 + -7.02020202x + x2 = 0 + 5.050505051 Combine like terms: -5.050505051 + 5.050505051 = 0.000000000 0.000000000 + -7.02020202x + x2 = 0 + 5.050505051 -7.02020202x + x2 = 0 + 5.050505051 Combine like terms: 0 + 5.050505051 = 5.050505051 -7.02020202x + x2 = 5.050505051 The x term is -7.02020202x. Take half its coefficient (-3.51010101). Square it (12.32080910) and add it to both sides. Add '12.32080910' to each side of the equation. -7.02020202x + 12.32080910 + x2 = 5.050505051 + 12.32080910 Reorder the terms: 12.32080910 + -7.02020202x + x2 = 5.050505051 + 12.32080910 Combine like terms: 5.050505051 + 12.32080910 = 17.371314151 12.32080910 + -7.02020202x + x2 = 17.371314151 Factor a perfect square on the left side: (x + -3.51010101)(x + -3.51010101) = 17.371314151 Calculate the square root of the right side: 4.167890852 Break this problem into two subproblems by setting (x + -3.51010101) equal to 4.167890852 and -4.167890852.Subproblem 1
x + -3.51010101 = 4.167890852 Simplifying x + -3.51010101 = 4.167890852 Reorder the terms: -3.51010101 + x = 4.167890852 Solving -3.51010101 + x = 4.167890852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.51010101' to each side of the equation. -3.51010101 + 3.51010101 + x = 4.167890852 + 3.51010101 Combine like terms: -3.51010101 + 3.51010101 = 0.00000000 0.00000000 + x = 4.167890852 + 3.51010101 x = 4.167890852 + 3.51010101 Combine like terms: 4.167890852 + 3.51010101 = 7.677991862 x = 7.677991862 Simplifying x = 7.677991862Subproblem 2
x + -3.51010101 = -4.167890852 Simplifying x + -3.51010101 = -4.167890852 Reorder the terms: -3.51010101 + x = -4.167890852 Solving -3.51010101 + x = -4.167890852 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.51010101' to each side of the equation. -3.51010101 + 3.51010101 + x = -4.167890852 + 3.51010101 Combine like terms: -3.51010101 + 3.51010101 = 0.00000000 0.00000000 + x = -4.167890852 + 3.51010101 x = -4.167890852 + 3.51010101 Combine like terms: -4.167890852 + 3.51010101 = -0.657789842 x = -0.657789842 Simplifying x = -0.657789842Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.677991862, -0.657789842}
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