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Simplifying 1909 = 2 * 3.14r * 30 + 2 * 3.14r2 Reorder the terms for easier multiplication: 1909 = 2 * 3.14 * 30r + 2 * 3.14r2 Multiply 2 * 3.14 1909 = 6.28 * 30r + 2 * 3.14r2 Multiply 6.28 * 30 1909 = 188.4r + 2 * 3.14r2 Multiply 2 * 3.14 1909 = 188.4r + 6.28r2 Solving 1909 = 188.4r + 6.28r2 Solving for variable 'r'. Reorder the terms: 1909 + -188.4r + -6.28r2 = 188.4r + -188.4r + 6.28r2 + -6.28r2 Combine like terms: 188.4r + -188.4r = 0.0 1909 + -188.4r + -6.28r2 = 0.0 + 6.28r2 + -6.28r2 1909 + -188.4r + -6.28r2 = 6.28r2 + -6.28r2 Combine like terms: 6.28r2 + -6.28r2 = 0.00 1909 + -188.4r + -6.28r2 = 0.00 Begin completing the square. Divide all terms by -6.28 the coefficient of the squared term: Divide each side by '-6.28'. -303.9808917 + 30r + r2 = 0 Move the constant term to the right: Add '303.9808917' to each side of the equation. -303.9808917 + 30r + 303.9808917 + r2 = 0 + 303.9808917 Reorder the terms: -303.9808917 + 303.9808917 + 30r + r2 = 0 + 303.9808917 Combine like terms: -303.9808917 + 303.9808917 = 0.0000000 0.0000000 + 30r + r2 = 0 + 303.9808917 30r + r2 = 0 + 303.9808917 Combine like terms: 0 + 303.9808917 = 303.9808917 30r + r2 = 303.9808917 The r term is 30r. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30r + 225 + r2 = 303.9808917 + 225 Reorder the terms: 225 + 30r + r2 = 303.9808917 + 225 Combine like terms: 303.9808917 + 225 = 528.9808917 225 + 30r + r2 = 528.9808917 Factor a perfect square on the left side: (r + 15)(r + 15) = 528.9808917 Calculate the square root of the right side: 22.999584598 Break this problem into two subproblems by setting (r + 15) equal to 22.999584598 and -22.999584598.Subproblem 1
r + 15 = 22.999584598 Simplifying r + 15 = 22.999584598 Reorder the terms: 15 + r = 22.999584598 Solving 15 + r = 22.999584598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + r = 22.999584598 + -15 Combine like terms: 15 + -15 = 0 0 + r = 22.999584598 + -15 r = 22.999584598 + -15 Combine like terms: 22.999584598 + -15 = 7.999584598 r = 7.999584598 Simplifying r = 7.999584598Subproblem 2
r + 15 = -22.999584598 Simplifying r + 15 = -22.999584598 Reorder the terms: 15 + r = -22.999584598 Solving 15 + r = -22.999584598 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + r = -22.999584598 + -15 Combine like terms: 15 + -15 = 0 0 + r = -22.999584598 + -15 r = -22.999584598 + -15 Combine like terms: -22.999584598 + -15 = -37.999584598 r = -37.999584598 Simplifying r = -37.999584598Solution
The solution to the problem is based on the solutions from the subproblems. r = {7.999584598, -37.999584598}
| x/((0.30-x)(0.40-x))=4.26 | | 1909=2*3.14*r*30 | | x/(0.30-x)(0.40-x)=0 | | y=x^2+100 | | x-0.60x=6 | | 13=e^4x | | 2x^1/3-8=1 | | 46=47+-x | | g(14)=6/7(14)-4 | | x-x*(225-5-5x)+4-3x*5= | | 10(2x-1)=8(2x+1)+4 | | 9x+4x-2x=28+5 | | 7s+8s= | | -8x-11y-9x+6y= | | x-60x=56 | | 8x-(-13x)= | | x-20x=6 | | 4(3z+6)= | | 3(y-x)=2(y+x) | | 5(t-3)+7t=6(2t+3)-10 | | a-20=5 | | a+2.4=7 | | x-0.60x=56 | | (x+3)2=(x-2)2 | | y=1/3.5x-2 | | u=5(9n+31)+9(n+1) | | 99/23=25.5/x | | log(4x-3)=2.50 | | m+3=25 | | 8(3n-5)=(9n+4)+2 | | 99/12=25.5/x | | 1,5,4,2,50,10=477 |