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Simplifying 24x2 + -58x + 4 = 0 Reorder the terms: 4 + -58x + 24x2 = 0 Solving 4 + -58x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -29x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -29x + 12x2)' equal to zero and attempt to solve: Simplifying 2 + -29x + 12x2 = 0 Solving 2 + -29x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.1666666667 + -2.416666667x + x2 = 0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + -2.416666667x + -0.1666666667 + x2 = 0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + -2.416666667x + x2 = 0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + -2.416666667x + x2 = 0 + -0.1666666667 -2.416666667x + x2 = 0 + -0.1666666667 Combine like terms: 0 + -0.1666666667 = -0.1666666667 -2.416666667x + x2 = -0.1666666667 The x term is -2.416666667x. Take half its coefficient (-1.208333334). Square it (1.460069446) and add it to both sides. Add '1.460069446' to each side of the equation. -2.416666667x + 1.460069446 + x2 = -0.1666666667 + 1.460069446 Reorder the terms: 1.460069446 + -2.416666667x + x2 = -0.1666666667 + 1.460069446 Combine like terms: -0.1666666667 + 1.460069446 = 1.2934027793 1.460069446 + -2.416666667x + x2 = 1.2934027793 Factor a perfect square on the left side: (x + -1.208333334)(x + -1.208333334) = 1.2934027793 Calculate the square root of the right side: 1.137278673 Break this problem into two subproblems by setting (x + -1.208333334) equal to 1.137278673 and -1.137278673.Subproblem 1
x + -1.208333334 = 1.137278673 Simplifying x + -1.208333334 = 1.137278673 Reorder the terms: -1.208333334 + x = 1.137278673 Solving -1.208333334 + x = 1.137278673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = 1.137278673 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = 1.137278673 + 1.208333334 x = 1.137278673 + 1.208333334 Combine like terms: 1.137278673 + 1.208333334 = 2.345612007 x = 2.345612007 Simplifying x = 2.345612007Subproblem 2
x + -1.208333334 = -1.137278673 Simplifying x + -1.208333334 = -1.137278673 Reorder the terms: -1.208333334 + x = -1.137278673 Solving -1.208333334 + x = -1.137278673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.208333334' to each side of the equation. -1.208333334 + 1.208333334 + x = -1.137278673 + 1.208333334 Combine like terms: -1.208333334 + 1.208333334 = 0.000000000 0.000000000 + x = -1.137278673 + 1.208333334 x = -1.137278673 + 1.208333334 Combine like terms: -1.137278673 + 1.208333334 = 0.071054661 x = 0.071054661 Simplifying x = 0.071054661Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.345612007, 0.071054661}Solution
x = {2.345612007, 0.071054661}
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