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Simplifying 24x2 + -14x + -4 = 0 Reorder the terms: -4 + -14x + 24x2 = 0 Solving -4 + -14x + 24x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -7x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -7x + 12x2)' equal to zero and attempt to solve: Simplifying -2 + -7x + 12x2 = 0 Solving -2 + -7x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.1666666667 + -0.5833333333x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -0.5833333333x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -0.5833333333x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -0.5833333333x + x2 = 0 + 0.1666666667 -0.5833333333x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -0.5833333333x + x2 = 0.1666666667 The x term is -0.5833333333x. Take half its coefficient (-0.2916666667). Square it (0.08506944446) and add it to both sides. Add '0.08506944446' to each side of the equation. -0.5833333333x + 0.08506944446 + x2 = 0.1666666667 + 0.08506944446 Reorder the terms: 0.08506944446 + -0.5833333333x + x2 = 0.1666666667 + 0.08506944446 Combine like terms: 0.1666666667 + 0.08506944446 = 0.25173611116 0.08506944446 + -0.5833333333x + x2 = 0.25173611116 Factor a perfect square on the left side: (x + -0.2916666667)(x + -0.2916666667) = 0.25173611116 Calculate the square root of the right side: 0.501733107 Break this problem into two subproblems by setting (x + -0.2916666667) equal to 0.501733107 and -0.501733107.Subproblem 1
x + -0.2916666667 = 0.501733107 Simplifying x + -0.2916666667 = 0.501733107 Reorder the terms: -0.2916666667 + x = 0.501733107 Solving -0.2916666667 + x = 0.501733107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = 0.501733107 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = 0.501733107 + 0.2916666667 x = 0.501733107 + 0.2916666667 Combine like terms: 0.501733107 + 0.2916666667 = 0.7933997737 x = 0.7933997737 Simplifying x = 0.7933997737Subproblem 2
x + -0.2916666667 = -0.501733107 Simplifying x + -0.2916666667 = -0.501733107 Reorder the terms: -0.2916666667 + x = -0.501733107 Solving -0.2916666667 + x = -0.501733107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2916666667' to each side of the equation. -0.2916666667 + 0.2916666667 + x = -0.501733107 + 0.2916666667 Combine like terms: -0.2916666667 + 0.2916666667 = 0.0000000000 0.0000000000 + x = -0.501733107 + 0.2916666667 x = -0.501733107 + 0.2916666667 Combine like terms: -0.501733107 + 0.2916666667 = -0.2100664403 x = -0.2100664403 Simplifying x = -0.2100664403Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7933997737, -0.2100664403}Solution
x = {0.7933997737, -0.2100664403}
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