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Simplifying 225 = 324x2 + 540x Reorder the terms: 225 = 540x + 324x2 Solving 225 = 540x + 324x2 Solving for variable 'x'. Reorder the terms: 225 + -540x + -324x2 = 540x + -540x + 324x2 + -324x2 Combine like terms: 540x + -540x = 0 225 + -540x + -324x2 = 0 + 324x2 + -324x2 225 + -540x + -324x2 = 324x2 + -324x2 Combine like terms: 324x2 + -324x2 = 0 225 + -540x + -324x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(25 + -60x + -36x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(25 + -60x + -36x2)' equal to zero and attempt to solve: Simplifying 25 + -60x + -36x2 = 0 Solving 25 + -60x + -36x2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. -0.6944444444 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '0.6944444444' to each side of the equation. -0.6944444444 + 1.666666667x + 0.6944444444 + x2 = 0 + 0.6944444444 Reorder the terms: -0.6944444444 + 0.6944444444 + 1.666666667x + x2 = 0 + 0.6944444444 Combine like terms: -0.6944444444 + 0.6944444444 = 0.0000000000 0.0000000000 + 1.666666667x + x2 = 0 + 0.6944444444 1.666666667x + x2 = 0 + 0.6944444444 Combine like terms: 0 + 0.6944444444 = 0.6944444444 1.666666667x + x2 = 0.6944444444 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 0.6944444444 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 0.6944444444 + 0.6944444447 Combine like terms: 0.6944444444 + 0.6944444447 = 1.3888888891 0.6944444447 + 1.666666667x + x2 = 1.3888888891 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 1.3888888891 Calculate the square root of the right side: 1.178511302 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.178511302 and -1.178511302.Subproblem 1
x + 0.8333333335 = 1.178511302 Simplifying x + 0.8333333335 = 1.178511302 Reorder the terms: 0.8333333335 + x = 1.178511302 Solving 0.8333333335 + x = 1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.178511302 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.178511302 + -0.8333333335 x = 1.178511302 + -0.8333333335 Combine like terms: 1.178511302 + -0.8333333335 = 0.3451779685 x = 0.3451779685 Simplifying x = 0.3451779685Subproblem 2
x + 0.8333333335 = -1.178511302 Simplifying x + 0.8333333335 = -1.178511302 Reorder the terms: 0.8333333335 + x = -1.178511302 Solving 0.8333333335 + x = -1.178511302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.178511302 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.178511302 + -0.8333333335 x = -1.178511302 + -0.8333333335 Combine like terms: -1.178511302 + -0.8333333335 = -2.0118446355 x = -2.0118446355 Simplifying x = -2.0118446355Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3451779685, -2.0118446355}Solution
x = {0.3451779685, -2.0118446355}
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