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Simplifying 9 + 6n = 6n2 Solving 9 + 6n = 6n2 Solving for variable 'n'. Combine like terms: 6n2 + -6n2 = 0 9 + 6n + -6n2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + 2n + -2n2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 2n + -2n2)' equal to zero and attempt to solve: Simplifying 3 + 2n + -2n2 = 0 Solving 3 + 2n + -2n2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + -1n + n2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1n + 1.5 + n2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1n + n2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1n + n2 = 0 + 1.5 -1n + n2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1n + n2 = 1.5 The n term is -1n. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1n + 0.25 + n2 = 1.5 + 0.25 Reorder the terms: 0.25 + -1n + n2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1n + n2 = 1.75 Factor a perfect square on the left side: (n + -0.5)(n + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (n + -0.5) equal to 1.322875656 and -1.322875656.Subproblem 1
n + -0.5 = 1.322875656 Simplifying n + -0.5 = 1.322875656 Reorder the terms: -0.5 + n = 1.322875656 Solving -0.5 + n = 1.322875656 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = 1.322875656 + 0.5 n = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 n = 1.822875656 Simplifying n = 1.822875656Subproblem 2
n + -0.5 = -1.322875656 Simplifying n + -0.5 = -1.322875656 Reorder the terms: -0.5 + n = -1.322875656 Solving -0.5 + n = -1.322875656 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + n = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + n = -1.322875656 + 0.5 n = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 n = -0.822875656 Simplifying n = -0.822875656Solution
The solution to the problem is based on the solutions from the subproblems. n = {1.822875656, -0.822875656}Solution
n = {1.822875656, -0.822875656}
| 10/2=x+1/3 | | n-(12-n)=38 | | n*5.06=506.00 | | x^2+y^2-4x-8y+20=0 | | y-2=-4(x-1) | | 20-2p=5+3p | | .83333333333333333x-3=.625x+7 | | v+5/4=3/6 | | -2(3n-6)=-6 | | 2330100+x=2.1*(863000+x) | | 2(-c-12)=-2c-12 | | 17+4j=125 | | 10/5=4/x | | 14+20=28+13-13 | | 8+9=15y-5-14y | | x-.15x=180 | | 1.6h-72=30-4h | | .83x-3=.625x+7 | | (3x+6)+(x+2)+(x+2)+(3x+6)= | | 6519.8+150.99w=3500 | | 16-3x=6x+7 | | 48k=-276 | | 6x(2)+1-n+5n(2)= | | 6519.88-150.99w=3500 | | 3z+8=13+3x-z | | -2a-9=6a+5 | | 3500-150.99w=-6519.88 | | 2+2x+7=-6 | | 20+14=28+13 | | -49+3k=k-5k | | findy-7x+7y=105 | | 3500+150.99w=6519.88 |