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Simplifying 4x2 + -40x + 6 = 0 Reorder the terms: 6 + -40x + 4x2 = 0 Solving 6 + -40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -20x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -20x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -20x + 2x2 = 0 Solving 3 + -20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -10x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -10x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -10x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -10x + x2 = 0 + -1.5 -10x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -10x + x2 = -1.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -1.5 + 25 Reorder the terms: 25 + -10x + x2 = -1.5 + 25 Combine like terms: -1.5 + 25 = 23.5 25 + -10x + x2 = 23.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + -5) equal to 4.847679857 and -4.847679857.Subproblem 1
x + -5 = 4.847679857 Simplifying x + -5 = 4.847679857 Reorder the terms: -5 + x = 4.847679857 Solving -5 + x = 4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.847679857 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.847679857 + 5 x = 4.847679857 + 5 Combine like terms: 4.847679857 + 5 = 9.847679857 x = 9.847679857 Simplifying x = 9.847679857Subproblem 2
x + -5 = -4.847679857 Simplifying x + -5 = -4.847679857 Reorder the terms: -5 + x = -4.847679857 Solving -5 + x = -4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.847679857 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.847679857 + 5 x = -4.847679857 + 5 Combine like terms: -4.847679857 + 5 = 0.152320143 x = 0.152320143 Simplifying x = 0.152320143Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.847679857, 0.152320143}Solution
x = {9.847679857, 0.152320143}
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