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Simplifying 25x3 + -30x5 + 35x = 0 Reorder the terms: 35x + 25x3 + -30x5 = 0 Solving 35x + 25x3 + -30x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(7 + 5x2 + -6x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 5x2 + -6x4)' equal to zero and attempt to solve: Simplifying 7 + 5x2 + -6x4 = 0 Solving 7 + 5x2 + -6x4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -1.166666667 + -0.8333333333x2 + x4 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + -0.8333333333x2 + 1.166666667 + x4 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + -0.8333333333x2 + x4 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + -0.8333333333x2 + x4 = 0 + 1.166666667 -0.8333333333x2 + x4 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 -0.8333333333x2 + x4 = 1.166666667 The x term is -0.8333333333x2. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x2 + 0.1736111111 + x4 = 1.166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x2 + x4 = 1.166666667 + 0.1736111111 Combine like terms: 1.166666667 + 0.1736111111 = 1.3402777781 0.1736111111 + -0.8333333333x2 + x4 = 1.3402777781 Factor a perfect square on the left side: (x2 + -0.4166666667)(x2 + -0.4166666667) = 1.3402777781 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x2 + -0.4166666667) equal to 1.157703666 and -1.157703666.Subproblem 1
x2 + -0.4166666667 = 1.157703666 Simplifying x2 + -0.4166666667 = 1.157703666 Reorder the terms: -0.4166666667 + x2 = 1.157703666 Solving -0.4166666667 + x2 = 1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = 1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = 1.157703666 + 0.4166666667 x2 = 1.157703666 + 0.4166666667 Combine like terms: 1.157703666 + 0.4166666667 = 1.5743703327 x2 = 1.5743703327 Simplifying x2 = 1.5743703327 Take the square root of each side: x = {-1.254739149, 1.254739149}Subproblem 2
x2 + -0.4166666667 = -1.157703666 Simplifying x2 + -0.4166666667 = -1.157703666 Reorder the terms: -0.4166666667 + x2 = -1.157703666 Solving -0.4166666667 + x2 = -1.157703666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x2 = -1.157703666 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x2 = -1.157703666 + 0.4166666667 x2 = -1.157703666 + 0.4166666667 Combine like terms: -1.157703666 + 0.4166666667 = -0.7410369993 x2 = -0.7410369993 Simplifying x2 = -0.7410369993 Reorder the terms: 0.7410369993 + x2 = -0.7410369993 + 0.7410369993 Combine like terms: -0.7410369993 + 0.7410369993 = 0.0000000000 0.7410369993 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
| 9a(36-4a)= | | 7x+7y=7xy | | (-3f+12)*29= | | 0=18x-14 | | 7(a-1)= | | 6-(4z-4)=5-5z | | 4x^2+3y=37.75 | | AED=18x-14 | | 4-5x+3=3x+4 | | X(1+y)= | | x^2+(sqrt(10)-sqrt(30))x-10sqrt(3)=0 | | 8+8lnx=13 | | 16-2x+8x-14=180 | | 470+a=2.5 | | -2h-0.1=0.625 | | 2=LW | | 65=3x+3x | | 6x+4-x= | | 3x*72x+1=37 | | 4x+12=6x-20 | | m+3=3+m+4 | | 470-a=2.5 | | 7x-6=3(2x+1) | | 5x+7-3(x-1)=9x+6 | | -20+7f=20+5f | | 19+17+9k=-16+5k | | 2x^2+1-log(x)=0 | | 4b+8=20+b | | w*w*w*z*z*y*y= | | -3/4(8x-24)=4-(25/3)x | | 8y+5y-3y= | | 3.5x=18+1.5x |