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Simplifying 240x2 + 280x + -230 = 0 Reorder the terms: -230 + 280x + 240x2 = 0 Solving -230 + 280x + 240x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(-23 + 28x + 24x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-23 + 28x + 24x2)' equal to zero and attempt to solve: Simplifying -23 + 28x + 24x2 = 0 Solving -23 + 28x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.9583333333 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '0.9583333333' to each side of the equation. -0.9583333333 + 1.166666667x + 0.9583333333 + x2 = 0 + 0.9583333333 Reorder the terms: -0.9583333333 + 0.9583333333 + 1.166666667x + x2 = 0 + 0.9583333333 Combine like terms: -0.9583333333 + 0.9583333333 = 0.0000000000 0.0000000000 + 1.166666667x + x2 = 0 + 0.9583333333 1.166666667x + x2 = 0 + 0.9583333333 Combine like terms: 0 + 0.9583333333 = 0.9583333333 1.166666667x + x2 = 0.9583333333 The x term is 1.166666667x. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x + 0.3402777780 + x2 = 0.9583333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 0.9583333333 + 0.3402777780 Combine like terms: 0.9583333333 + 0.3402777780 = 1.2986111113 0.3402777780 + 1.166666667x + x2 = 1.2986111113 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.2986111113 Calculate the square root of the right side: 1.139566194 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.139566194 and -1.139566194.Subproblem 1
x + 0.5833333335 = 1.139566194 Simplifying x + 0.5833333335 = 1.139566194 Reorder the terms: 0.5833333335 + x = 1.139566194 Solving 0.5833333335 + x = 1.139566194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = 1.139566194 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.139566194 + -0.5833333335 x = 1.139566194 + -0.5833333335 Combine like terms: 1.139566194 + -0.5833333335 = 0.5562328605 x = 0.5562328605 Simplifying x = 0.5562328605Subproblem 2
x + 0.5833333335 = -1.139566194 Simplifying x + 0.5833333335 = -1.139566194 Reorder the terms: 0.5833333335 + x = -1.139566194 Solving 0.5833333335 + x = -1.139566194 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x = -1.139566194 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.139566194 + -0.5833333335 x = -1.139566194 + -0.5833333335 Combine like terms: -1.139566194 + -0.5833333335 = -1.7228995275 x = -1.7228995275 Simplifying x = -1.7228995275Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5562328605, -1.7228995275}Solution
x = {0.5562328605, -1.7228995275}
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