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Simplifying 45x2 + -90x + -20 = 0 Reorder the terms: -20 + -90x + 45x2 = 0 Solving -20 + -90x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + -18x + 9x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -18x + 9x2)' equal to zero and attempt to solve: Simplifying -4 + -18x + 9x2 = 0 Solving -4 + -18x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -2x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -2x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -2x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + 0.4444444444 -2x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -2x + x2 = 0.4444444444 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.4444444444 + 1 Reorder the terms: 1 + -2x + x2 = 0.4444444444 + 1 Combine like terms: 0.4444444444 + 1 = 1.4444444444 1 + -2x + x2 = 1.4444444444 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.4444444444 Calculate the square root of the right side: 1.201850425 Break this problem into two subproblems by setting (x + -1) equal to 1.201850425 and -1.201850425.Subproblem 1
x + -1 = 1.201850425 Simplifying x + -1 = 1.201850425 Reorder the terms: -1 + x = 1.201850425 Solving -1 + x = 1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.201850425 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.201850425 + 1 x = 1.201850425 + 1 Combine like terms: 1.201850425 + 1 = 2.201850425 x = 2.201850425 Simplifying x = 2.201850425Subproblem 2
x + -1 = -1.201850425 Simplifying x + -1 = -1.201850425 Reorder the terms: -1 + x = -1.201850425 Solving -1 + x = -1.201850425 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.201850425 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.201850425 + 1 x = -1.201850425 + 1 Combine like terms: -1.201850425 + 1 = -0.201850425 x = -0.201850425 Simplifying x = -0.201850425Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.201850425, -0.201850425}Solution
x = {2.201850425, -0.201850425}
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