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Simplifying 120x2 + -9x + -21 = 0 Reorder the terms: -21 + -9x + 120x2 = 0 Solving -21 + -9x + 120x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-7 + -3x + 40x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-7 + -3x + 40x2)' equal to zero and attempt to solve: Simplifying -7 + -3x + 40x2 = 0 Solving -7 + -3x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.175 + -0.075x + x2 = 0.0 Move the constant term to the right: Add '0.175' to each side of the equation. -0.175 + -0.075x + 0.175 + x2 = 0.0 + 0.175 Reorder the terms: -0.175 + 0.175 + -0.075x + x2 = 0.0 + 0.175 Combine like terms: -0.175 + 0.175 = 0.000 0.000 + -0.075x + x2 = 0.0 + 0.175 -0.075x + x2 = 0.0 + 0.175 Combine like terms: 0.0 + 0.175 = 0.175 -0.075x + x2 = 0.175 The x term is -0.075x. Take half its coefficient (-0.0375). Square it (0.00140625) and add it to both sides. Add '0.00140625' to each side of the equation. -0.075x + 0.00140625 + x2 = 0.175 + 0.00140625 Reorder the terms: 0.00140625 + -0.075x + x2 = 0.175 + 0.00140625 Combine like terms: 0.175 + 0.00140625 = 0.17640625 0.00140625 + -0.075x + x2 = 0.17640625 Factor a perfect square on the left side: (x + -0.0375)(x + -0.0375) = 0.17640625 Calculate the square root of the right side: 0.42000744 Break this problem into two subproblems by setting (x + -0.0375) equal to 0.42000744 and -0.42000744.Subproblem 1
x + -0.0375 = 0.42000744 Simplifying x + -0.0375 = 0.42000744 Reorder the terms: -0.0375 + x = 0.42000744 Solving -0.0375 + x = 0.42000744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = 0.42000744 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = 0.42000744 + 0.0375 x = 0.42000744 + 0.0375 Combine like terms: 0.42000744 + 0.0375 = 0.45750744 x = 0.45750744 Simplifying x = 0.45750744Subproblem 2
x + -0.0375 = -0.42000744 Simplifying x + -0.0375 = -0.42000744 Reorder the terms: -0.0375 + x = -0.42000744 Solving -0.0375 + x = -0.42000744 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0375' to each side of the equation. -0.0375 + 0.0375 + x = -0.42000744 + 0.0375 Combine like terms: -0.0375 + 0.0375 = 0.0000 0.0000 + x = -0.42000744 + 0.0375 x = -0.42000744 + 0.0375 Combine like terms: -0.42000744 + 0.0375 = -0.38250744 x = -0.38250744 Simplifying x = -0.38250744Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.45750744, -0.38250744}Solution
x = {0.45750744, -0.38250744}
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