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Simplifying 45x2 + -435x + 180 = 0 Reorder the terms: 180 + -435x + 45x2 = 0 Solving 180 + -435x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(12 + -29x + 3x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(12 + -29x + 3x2)' equal to zero and attempt to solve: Simplifying 12 + -29x + 3x2 = 0 Solving 12 + -29x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -9.666666667x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -9.666666667x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -9.666666667x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9.666666667x + x2 = 0 + -4 -9.666666667x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -9.666666667x + x2 = -4 The x term is -9.666666667x. Take half its coefficient (-4.833333334). Square it (23.36111112) and add it to both sides. Add '23.36111112' to each side of the equation. -9.666666667x + 23.36111112 + x2 = -4 + 23.36111112 Reorder the terms: 23.36111112 + -9.666666667x + x2 = -4 + 23.36111112 Combine like terms: -4 + 23.36111112 = 19.36111112 23.36111112 + -9.666666667x + x2 = 19.36111112 Factor a perfect square on the left side: (x + -4.833333334)(x + -4.833333334) = 19.36111112 Calculate the square root of the right side: 4.400126262 Break this problem into two subproblems by setting (x + -4.833333334) equal to 4.400126262 and -4.400126262.Subproblem 1
x + -4.833333334 = 4.400126262 Simplifying x + -4.833333334 = 4.400126262 Reorder the terms: -4.833333334 + x = 4.400126262 Solving -4.833333334 + x = 4.400126262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = 4.400126262 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = 4.400126262 + 4.833333334 x = 4.400126262 + 4.833333334 Combine like terms: 4.400126262 + 4.833333334 = 9.233459596 x = 9.233459596 Simplifying x = 9.233459596Subproblem 2
x + -4.833333334 = -4.400126262 Simplifying x + -4.833333334 = -4.400126262 Reorder the terms: -4.833333334 + x = -4.400126262 Solving -4.833333334 + x = -4.400126262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.833333334' to each side of the equation. -4.833333334 + 4.833333334 + x = -4.400126262 + 4.833333334 Combine like terms: -4.833333334 + 4.833333334 = 0.000000000 0.000000000 + x = -4.400126262 + 4.833333334 x = -4.400126262 + 4.833333334 Combine like terms: -4.400126262 + 4.833333334 = 0.433207072 x = 0.433207072 Simplifying x = 0.433207072Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.233459596, 0.433207072}Solution
x = {9.233459596, 0.433207072}
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