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Simplifying -18x5 + -16x4 + 75x3 = 0 Reorder the terms: 75x3 + -16x4 + -18x5 = 0 Solving 75x3 + -16x4 + -18x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(75 + -16x + -18x2) = 0Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(75 + -16x + -18x2)' equal to zero and attempt to solve: Simplifying 75 + -16x + -18x2 = 0 Solving 75 + -16x + -18x2 = 0 Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -4.166666667 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 0.8888888889x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 0.8888888889x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 0.8888888889x + x2 = 0 + 4.166666667 0.8888888889x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 0.8888888889x + x2 = 4.166666667 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 4.166666667 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 4.166666667 + 0.1975308642 Combine like terms: 4.166666667 + 0.1975308642 = 4.3641975312 0.1975308642 + 0.8888888889x + x2 = 4.3641975312 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 4.3641975312 Calculate the square root of the right side: 2.089066186 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 2.089066186 and -2.089066186.Subproblem 1
x + 0.4444444445 = 2.089066186 Simplifying x + 0.4444444445 = 2.089066186 Reorder the terms: 0.4444444445 + x = 2.089066186 Solving 0.4444444445 + x = 2.089066186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 2.089066186 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 2.089066186 + -0.4444444445 x = 2.089066186 + -0.4444444445 Combine like terms: 2.089066186 + -0.4444444445 = 1.6446217415 x = 1.6446217415 Simplifying x = 1.6446217415Subproblem 2
x + 0.4444444445 = -2.089066186 Simplifying x + 0.4444444445 = -2.089066186 Reorder the terms: 0.4444444445 + x = -2.089066186 Solving 0.4444444445 + x = -2.089066186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -2.089066186 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -2.089066186 + -0.4444444445 x = -2.089066186 + -0.4444444445 Combine like terms: -2.089066186 + -0.4444444445 = -2.5335106305 x = -2.5335106305 Simplifying x = -2.5335106305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6446217415, -2.5335106305}Solution
x = {1.6446217415, -2.5335106305}
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