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Simplifying 270x2 + 99x + -30 = 0 Reorder the terms: -30 + 99x + 270x2 = 0 Solving -30 + 99x + 270x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-10 + 33x + 90x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10 + 33x + 90x2)' equal to zero and attempt to solve: Simplifying -10 + 33x + 90x2 = 0 Solving -10 + 33x + 90x2 = 0 Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. -0.1111111111 + 0.3666666667x + x2 = 0.0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.3666666667x + 0.1111111111 + x2 = 0.0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + 0.3666666667x + x2 = 0.0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + 0.3666666667x + x2 = 0.0 + 0.1111111111 0.3666666667x + x2 = 0.0 + 0.1111111111 Combine like terms: 0.0 + 0.1111111111 = 0.1111111111 0.3666666667x + x2 = 0.1111111111 The x term is 0.3666666667x. Take half its coefficient (0.1833333334). Square it (0.03361111114) and add it to both sides. Add '0.03361111114' to each side of the equation. 0.3666666667x + 0.03361111114 + x2 = 0.1111111111 + 0.03361111114 Reorder the terms: 0.03361111114 + 0.3666666667x + x2 = 0.1111111111 + 0.03361111114 Combine like terms: 0.1111111111 + 0.03361111114 = 0.14472222224 0.03361111114 + 0.3666666667x + x2 = 0.14472222224 Factor a perfect square on the left side: (x + 0.1833333334)(x + 0.1833333334) = 0.14472222224 Calculate the square root of the right side: 0.38042374 Break this problem into two subproblems by setting (x + 0.1833333334) equal to 0.38042374 and -0.38042374.Subproblem 1
x + 0.1833333334 = 0.38042374 Simplifying x + 0.1833333334 = 0.38042374 Reorder the terms: 0.1833333334 + x = 0.38042374 Solving 0.1833333334 + x = 0.38042374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1833333334' to each side of the equation. 0.1833333334 + -0.1833333334 + x = 0.38042374 + -0.1833333334 Combine like terms: 0.1833333334 + -0.1833333334 = 0.0000000000 0.0000000000 + x = 0.38042374 + -0.1833333334 x = 0.38042374 + -0.1833333334 Combine like terms: 0.38042374 + -0.1833333334 = 0.1970904066 x = 0.1970904066 Simplifying x = 0.1970904066Subproblem 2
x + 0.1833333334 = -0.38042374 Simplifying x + 0.1833333334 = -0.38042374 Reorder the terms: 0.1833333334 + x = -0.38042374 Solving 0.1833333334 + x = -0.38042374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1833333334' to each side of the equation. 0.1833333334 + -0.1833333334 + x = -0.38042374 + -0.1833333334 Combine like terms: 0.1833333334 + -0.1833333334 = 0.0000000000 0.0000000000 + x = -0.38042374 + -0.1833333334 x = -0.38042374 + -0.1833333334 Combine like terms: -0.38042374 + -0.1833333334 = -0.5637570734 x = -0.5637570734 Simplifying x = -0.5637570734Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1970904066, -0.5637570734}Solution
x = {0.1970904066, -0.5637570734}
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