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Simplifying 80 = -0.591x2 + 17.432x + -26.216 Reorder the terms: 80 = -26.216 + 17.432x + -0.591x2 Solving 80 = -26.216 + 17.432x + -0.591x2 Solving for variable 'x'. Combine like terms: 80 + 26.216 = 106.216 106.216 + -17.432x + 0.591x2 = -26.216 + 17.432x + -0.591x2 + 26.216 + -17.432x + 0.591x2 Reorder the terms: 106.216 + -17.432x + 0.591x2 = -26.216 + 26.216 + 17.432x + -17.432x + -0.591x2 + 0.591x2 Combine like terms: -26.216 + 26.216 = 0.000 106.216 + -17.432x + 0.591x2 = 0.000 + 17.432x + -17.432x + -0.591x2 + 0.591x2 106.216 + -17.432x + 0.591x2 = 17.432x + -17.432x + -0.591x2 + 0.591x2 Combine like terms: 17.432x + -17.432x = 0.000 106.216 + -17.432x + 0.591x2 = 0.000 + -0.591x2 + 0.591x2 106.216 + -17.432x + 0.591x2 = -0.591x2 + 0.591x2 Combine like terms: -0.591x2 + 0.591x2 = 0.000 106.216 + -17.432x + 0.591x2 = 0.000 Begin completing the square. Divide all terms by 0.591 the coefficient of the squared term: Divide each side by '0.591'. 179.7225042 + -29.49576988x + x2 = 0 Move the constant term to the right: Add '-179.7225042' to each side of the equation. 179.7225042 + -29.49576988x + -179.7225042 + x2 = 0 + -179.7225042 Reorder the terms: 179.7225042 + -179.7225042 + -29.49576988x + x2 = 0 + -179.7225042 Combine like terms: 179.7225042 + -179.7225042 = 0.0000000 0.0000000 + -29.49576988x + x2 = 0 + -179.7225042 -29.49576988x + x2 = 0 + -179.7225042 Combine like terms: 0 + -179.7225042 = -179.7225042 -29.49576988x + x2 = -179.7225042 The x term is -29.49576988x. Take half its coefficient (-14.74788494). Square it (217.5001102) and add it to both sides. Add '217.5001102' to each side of the equation. -29.49576988x + 217.5001102 + x2 = -179.7225042 + 217.5001102 Reorder the terms: 217.5001102 + -29.49576988x + x2 = -179.7225042 + 217.5001102 Combine like terms: -179.7225042 + 217.5001102 = 37.777606 217.5001102 + -29.49576988x + x2 = 37.777606 Factor a perfect square on the left side: (x + -14.74788494)(x + -14.74788494) = 37.777606 Calculate the square root of the right side: 6.146348998 Break this problem into two subproblems by setting (x + -14.74788494) equal to 6.146348998 and -6.146348998.Subproblem 1
x + -14.74788494 = 6.146348998 Simplifying x + -14.74788494 = 6.146348998 Reorder the terms: -14.74788494 + x = 6.146348998 Solving -14.74788494 + x = 6.146348998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.74788494' to each side of the equation. -14.74788494 + 14.74788494 + x = 6.146348998 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = 6.146348998 + 14.74788494 x = 6.146348998 + 14.74788494 Combine like terms: 6.146348998 + 14.74788494 = 20.894233938 x = 20.894233938 Simplifying x = 20.894233938Subproblem 2
x + -14.74788494 = -6.146348998 Simplifying x + -14.74788494 = -6.146348998 Reorder the terms: -14.74788494 + x = -6.146348998 Solving -14.74788494 + x = -6.146348998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.74788494' to each side of the equation. -14.74788494 + 14.74788494 + x = -6.146348998 + 14.74788494 Combine like terms: -14.74788494 + 14.74788494 = 0.00000000 0.00000000 + x = -6.146348998 + 14.74788494 x = -6.146348998 + 14.74788494 Combine like terms: -6.146348998 + 14.74788494 = 8.601535942 x = 8.601535942 Simplifying x = 8.601535942Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.894233938, 8.601535942}
| 2x+54+5x+7=180 | | m+6=13/2 | | d+3=30/11 | | d-1/2=-5/2 | | n+8/9=7/18 | | 3/8=d-3/8 | | d-1/2=-3/2 | | k+7/10=41/30 | | w+5/9=5/9 | | x/-4=6 | | 1/4t=-3/2 | | 2x=90-x | | b+5=6 | | 6+x=41/7 | | k-6/7=-115/77 | | 3b=3 | | -1/3+k=4/15 | | t-2/5=-7/5 | | -2/3n=4/27 | | 5(x-6)=3x+2 | | 20=-0.591x^2+17.432x-26.216 | | d+1/2=4/3 | | t-1/10=-61/10 | | w/7=-2/3 | | k-3/4=41/4 | | 59/9=b+6 | | x-8/9=-1/9 | | 3/4+k=27/4 | | 1/3+b=-8/3 | | m+1=6 | | b+4/9=38/45 | | n+1/5=-14/5 |