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Simplifying (0.64 + -3.2x + 4x2) * 0.016 + -1x2 = 0 Reorder the terms for easier multiplication: 0.016(0.64 + -3.2x + 4x2) + -1x2 = 0 (0.64 * 0.016 + -3.2x * 0.016 + 4x2 * 0.016) + -1x2 = 0 (0.01024 + -0.0512x + 0.064x2) + -1x2 = 0 Combine like terms: 0.064x2 + -1x2 = -0.936x2 0.01024 + -0.0512x + -0.936x2 = 0 Solving 0.01024 + -0.0512x + -0.936x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.936 the coefficient of the squared term: Divide each side by '-0.936'. -0.01094017094 + 0.0547008547x + x2 = 0 Move the constant term to the right: Add '0.01094017094' to each side of the equation. -0.01094017094 + 0.0547008547x + 0.01094017094 + x2 = 0 + 0.01094017094 Reorder the terms: -0.01094017094 + 0.01094017094 + 0.0547008547x + x2 = 0 + 0.01094017094 Combine like terms: -0.01094017094 + 0.01094017094 = 0.00000000000 0.00000000000 + 0.0547008547x + x2 = 0 + 0.01094017094 0.0547008547x + x2 = 0 + 0.01094017094 Combine like terms: 0 + 0.01094017094 = 0.01094017094 0.0547008547x + x2 = 0.01094017094 The x term is 0.0547008547x. Take half its coefficient (0.02735042735). Square it (0.0007480458762) and add it to both sides. Add '0.0007480458762' to each side of the equation. 0.0547008547x + 0.0007480458762 + x2 = 0.01094017094 + 0.0007480458762 Reorder the terms: 0.0007480458762 + 0.0547008547x + x2 = 0.01094017094 + 0.0007480458762 Combine like terms: 0.01094017094 + 0.0007480458762 = 0.0116882168162 0.0007480458762 + 0.0547008547x + x2 = 0.0116882168162 Factor a perfect square on the left side: (x + 0.02735042735)(x + 0.02735042735) = 0.0116882168162 Calculate the square root of the right side: 0.108112057 Break this problem into two subproblems by setting (x + 0.02735042735) equal to 0.108112057 and -0.108112057.Subproblem 1
x + 0.02735042735 = 0.108112057 Simplifying x + 0.02735042735 = 0.108112057 Reorder the terms: 0.02735042735 + x = 0.108112057 Solving 0.02735042735 + x = 0.108112057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02735042735' to each side of the equation. 0.02735042735 + -0.02735042735 + x = 0.108112057 + -0.02735042735 Combine like terms: 0.02735042735 + -0.02735042735 = 0.00000000000 0.00000000000 + x = 0.108112057 + -0.02735042735 x = 0.108112057 + -0.02735042735 Combine like terms: 0.108112057 + -0.02735042735 = 0.08076162965 x = 0.08076162965 Simplifying x = 0.08076162965Subproblem 2
x + 0.02735042735 = -0.108112057 Simplifying x + 0.02735042735 = -0.108112057 Reorder the terms: 0.02735042735 + x = -0.108112057 Solving 0.02735042735 + x = -0.108112057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02735042735' to each side of the equation. 0.02735042735 + -0.02735042735 + x = -0.108112057 + -0.02735042735 Combine like terms: 0.02735042735 + -0.02735042735 = 0.00000000000 0.00000000000 + x = -0.108112057 + -0.02735042735 x = -0.108112057 + -0.02735042735 Combine like terms: -0.108112057 + -0.02735042735 = -0.13546248435 x = -0.13546248435 Simplifying x = -0.13546248435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.08076162965, -0.13546248435}
| (0.64+-3.2x+4x^2)0.016=0 | | 2x+40=5.5 | | -6x-2=118 | | 38.79(10.99+4x)=60.77 | | 7x-5+5x+27=180 | | (0.8-2x)(0.8-2x)=0 | | 4y=-6+27x | | 1270.44=2*3.14*r^2+2*3.14*r*21.9 | | 4x+6=114 | | 5x-2(-1-3x)=0 | | 9x-7+3x+7=90 | | (siny-sinx)dx+((1+x)cosy)dy=0 | | 0.8(8x+5)=1.1-(x-3) | | 15*m=15 | | 7p+5+(-1)= | | 10x+0.10=x+0.35 | | 1=5.2x+58.2 | | 2x+17=-7x+53 | | 38.79(10.99-4x)=60.77 | | 10.99(4x+38.79)=60.77 | | 4x-2(x-4)=-7+5x+9 | | 4x(5w)= | | y=-8-4x | | 3a^2+11a+15=0 | | 10.99(2x+38.79)=60.77 | | y=3x^2-8x-60 | | 26+9x=1 | | 2x+3y=5x-5 | | 10.99(2x-60.77)=38.79 | | 8=3+25t-5t^2 | | 26+9=1 | | 60.77(2x+10.99)=38.79 |