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Simplifying 18x2 + -1x + -75 = 0 Reorder the terms: -75 + -1x + 18x2 = 0 Solving -75 + -1x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.166666667 + -0.05555555556x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -0.05555555556x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -0.05555555556x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -0.05555555556x + x2 = 0 + 4.166666667 -0.05555555556x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -0.05555555556x + x2 = 4.166666667 The x term is -0.05555555556x. Take half its coefficient (-0.02777777778). Square it (0.0007716049384) and add it to both sides. Add '0.0007716049384' to each side of the equation. -0.05555555556x + 0.0007716049384 + x2 = 4.166666667 + 0.0007716049384 Reorder the terms: 0.0007716049384 + -0.05555555556x + x2 = 4.166666667 + 0.0007716049384 Combine like terms: 4.166666667 + 0.0007716049384 = 4.1674382719384 0.0007716049384 + -0.05555555556x + x2 = 4.1674382719384 Factor a perfect square on the left side: (x + -0.02777777778)(x + -0.02777777778) = 4.1674382719384 Calculate the square root of the right side: 2.041430447 Break this problem into two subproblems by setting (x + -0.02777777778) equal to 2.041430447 and -2.041430447.Subproblem 1
x + -0.02777777778 = 2.041430447 Simplifying x + -0.02777777778 = 2.041430447 Reorder the terms: -0.02777777778 + x = 2.041430447 Solving -0.02777777778 + x = 2.041430447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = 2.041430447 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = 2.041430447 + 0.02777777778 x = 2.041430447 + 0.02777777778 Combine like terms: 2.041430447 + 0.02777777778 = 2.06920822478 x = 2.06920822478 Simplifying x = 2.06920822478Subproblem 2
x + -0.02777777778 = -2.041430447 Simplifying x + -0.02777777778 = -2.041430447 Reorder the terms: -0.02777777778 + x = -2.041430447 Solving -0.02777777778 + x = -2.041430447 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.02777777778 + x = -2.041430447 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + x = -2.041430447 + 0.02777777778 x = -2.041430447 + 0.02777777778 Combine like terms: -2.041430447 + 0.02777777778 = -2.01365266922 x = -2.01365266922 Simplifying x = -2.01365266922Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.06920822478, -2.01365266922}
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