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Simplifying 2x + -18x2 = 18x + -162 Reorder the terms: 2x + -18x2 = -162 + 18x Solving 2x + -18x2 = -162 + 18x Solving for variable 'x'. Reorder the terms: 162 + 2x + -18x + -18x2 = -162 + 18x + 162 + -18x Combine like terms: 2x + -18x = -16x 162 + -16x + -18x2 = -162 + 18x + 162 + -18x Reorder the terms: 162 + -16x + -18x2 = -162 + 162 + 18x + -18x Combine like terms: -162 + 162 = 0 162 + -16x + -18x2 = 0 + 18x + -18x 162 + -16x + -18x2 = 18x + -18x Combine like terms: 18x + -18x = 0 162 + -16x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(81 + -8x + -9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(81 + -8x + -9x2)' equal to zero and attempt to solve: Simplifying 81 + -8x + -9x2 = 0 Solving 81 + -8x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -9 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + 0.8888888889x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 0.8888888889x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 0.8888888889x + x2 = 0 + 9 0.8888888889x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 0.8888888889x + x2 = 9 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 = 9 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 9 + 0.1975308642 Combine like terms: 9 + 0.1975308642 = 9.1975308642 0.1975308642 + 0.8888888889x + x2 = 9.1975308642 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 9.1975308642 Calculate the square root of the right side: 3.032743125 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 3.032743125 and -3.032743125.Subproblem 1
x + 0.4444444445 = 3.032743125 Simplifying x + 0.4444444445 = 3.032743125 Reorder the terms: 0.4444444445 + x = 3.032743125 Solving 0.4444444445 + x = 3.032743125 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 = 3.032743125 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 3.032743125 + -0.4444444445 x = 3.032743125 + -0.4444444445 Combine like terms: 3.032743125 + -0.4444444445 = 2.5882986805 x = 2.5882986805 Simplifying x = 2.5882986805Subproblem 2
x + 0.4444444445 = -3.032743125 Simplifying x + 0.4444444445 = -3.032743125 Reorder the terms: 0.4444444445 + x = -3.032743125 Solving 0.4444444445 + x = -3.032743125 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 = -3.032743125 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -3.032743125 + -0.4444444445 x = -3.032743125 + -0.4444444445 Combine like terms: -3.032743125 + -0.4444444445 = -3.4771875695 x = -3.4771875695 Simplifying x = -3.4771875695Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5882986805, -3.4771875695}Solution
x = {2.5882986805, -3.4771875695}
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