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Simplifying 50 = -23.944 + 0.199x + -0.00008x2 Solving 50 = -23.944 + 0.199x + -0.00008x2 Solving for variable 'x'. Combine like terms: 50 + 23.944 = 73.944 73.944 + -0.199x + 0.00008x2 = -23.944 + 0.199x + -0.00008x2 + 23.944 + -0.199x + 0.00008x2 Reorder the terms: 73.944 + -0.199x + 0.00008x2 = -23.944 + 23.944 + 0.199x + -0.199x + -0.00008x2 + 0.00008x2 Combine like terms: -23.944 + 23.944 = 0.000 73.944 + -0.199x + 0.00008x2 = 0.000 + 0.199x + -0.199x + -0.00008x2 + 0.00008x2 73.944 + -0.199x + 0.00008x2 = 0.199x + -0.199x + -0.00008x2 + 0.00008x2 Combine like terms: 0.199x + -0.199x = 0.000 73.944 + -0.199x + 0.00008x2 = 0.000 + -0.00008x2 + 0.00008x2 73.944 + -0.199x + 0.00008x2 = -0.00008x2 + 0.00008x2 Combine like terms: -0.00008x2 + 0.00008x2 = 0.00000 73.944 + -0.199x + 0.00008x2 = 0.00000 Begin completing the square. Divide all terms by 0.00008 the coefficient of the squared term: Divide each side by '0.00008'. 924300 + -2487.5x + x2 = 0 Move the constant term to the right: Add '-924300' to each side of the equation. 924300 + -2487.5x + -924300 + x2 = 0 + -924300 Reorder the terms: 924300 + -924300 + -2487.5x + x2 = 0 + -924300 Combine like terms: 924300 + -924300 = 0 0 + -2487.5x + x2 = 0 + -924300 -2487.5x + x2 = 0 + -924300 Combine like terms: 0 + -924300 = -924300 -2487.5x + x2 = -924300 The x term is -2487.5x. Take half its coefficient (-1243.75). Square it (1546914.063) and add it to both sides. Add '1546914.063' to each side of the equation. -2487.5x + 1546914.063 + x2 = -924300 + 1546914.063 Reorder the terms: 1546914.063 + -2487.5x + x2 = -924300 + 1546914.063 Combine like terms: -924300 + 1546914.063 = 622614.063 1546914.063 + -2487.5x + x2 = 622614.063 Factor a perfect square on the left side: (x + -1243.75)(x + -1243.75) = 622614.063 Calculate the square root of the right side: 789.058973081 Break this problem into two subproblems by setting (x + -1243.75) equal to 789.058973081 and -789.058973081.Subproblem 1
x + -1243.75 = 789.058973081 Simplifying x + -1243.75 = 789.058973081 Reorder the terms: -1243.75 + x = 789.058973081 Solving -1243.75 + x = 789.058973081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1243.75' to each side of the equation. -1243.75 + 1243.75 + x = 789.058973081 + 1243.75 Combine like terms: -1243.75 + 1243.75 = 0.00 0.00 + x = 789.058973081 + 1243.75 x = 789.058973081 + 1243.75 Combine like terms: 789.058973081 + 1243.75 = 2032.808973081 x = 2032.808973081 Simplifying x = 2032.808973081Subproblem 2
x + -1243.75 = -789.058973081 Simplifying x + -1243.75 = -789.058973081 Reorder the terms: -1243.75 + x = -789.058973081 Solving -1243.75 + x = -789.058973081 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1243.75' to each side of the equation. -1243.75 + 1243.75 + x = -789.058973081 + 1243.75 Combine like terms: -1243.75 + 1243.75 = 0.00 0.00 + x = -789.058973081 + 1243.75 x = -789.058973081 + 1243.75 Combine like terms: -789.058973081 + 1243.75 = 454.691026919 x = 454.691026919 Simplifying x = 454.691026919Solution
The solution to the problem is based on the solutions from the subproblems. x = {2032.808973081, 454.691026919}
| 7m-(2m-n)= | | 4(2y-5)=20 | | 6-1/5w=21/5 | | 3/7k+10=82/7 | | 3/7+4b=13/14 | | 4/5a+2/3=58/15 | | 7d+3=38 | | 5b-9=-29 | | 1/3m+3=19/3 | | (x+5)(x-8)=(x-7)(x-2) | | -2/5t+2=7/3 | | 2k-8=-12 | | 3k-9=-87/10 | | 10+2b=104/9 | | 1/6b-6/7=41/42 | | -7d+5/7=-34/21 | | 3w-9=-87/11 | | y=-8*0.00001x^2+0.199x-23.944 | | 5m+1/8=321/8 | | 3/5n+8/9=643/450 | | 1/2-t=5/2 | | -d+8=11 | | 7m+1=71 | | 4x-2=6/5 | | 6(x+7)=-12(x-5) | | 3/7a+1=43/7 | | 5/7x-1/5=-59/420 | | 9+2k=54/5 | | -5t-3/4=-21/8 | | -2/7-b=68/7 | | -5/7a+4/7=58/49 | | 2/7n+8=115/14 |