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Simplifying 40x2 + 96x + 10 = 0 Reorder the terms: 10 + 96x + 40x2 = 0 Solving 10 + 96x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 48x + 20x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 48x + 20x2)' equal to zero and attempt to solve: Simplifying 5 + 48x + 20x2 = 0 Solving 5 + 48x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.25 + 2.4x + x2 = 0.0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 2.4x + -0.25 + x2 = 0.0 + -0.25 Reorder the terms: 0.25 + -0.25 + 2.4x + x2 = 0.0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 2.4x + x2 = 0.0 + -0.25 2.4x + x2 = 0.0 + -0.25 Combine like terms: 0.0 + -0.25 = -0.25 2.4x + x2 = -0.25 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = -0.25 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = -0.25 + 1.44 Combine like terms: -0.25 + 1.44 = 1.19 1.44 + 2.4x + x2 = 1.19 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 1.19 Calculate the square root of the right side: 1.090871211 Break this problem into two subproblems by setting (x + 1.2) equal to 1.090871211 and -1.090871211.Subproblem 1
x + 1.2 = 1.090871211 Simplifying x + 1.2 = 1.090871211 Reorder the terms: 1.2 + x = 1.090871211 Solving 1.2 + x = 1.090871211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.090871211 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.090871211 + -1.2 x = 1.090871211 + -1.2 Combine like terms: 1.090871211 + -1.2 = -0.109128789 x = -0.109128789 Simplifying x = -0.109128789Subproblem 2
x + 1.2 = -1.090871211 Simplifying x + 1.2 = -1.090871211 Reorder the terms: 1.2 + x = -1.090871211 Solving 1.2 + x = -1.090871211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.090871211 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.090871211 + -1.2 x = -1.090871211 + -1.2 Combine like terms: -1.090871211 + -1.2 = -2.290871211 x = -2.290871211 Simplifying x = -2.290871211Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.109128789, -2.290871211}Solution
x = {-0.109128789, -2.290871211}
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