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Simplifying 4x2 + -42x = 40 Reorder the terms: -42x + 4x2 = 40 Solving -42x + 4x2 = 40 Solving for variable 'x'. Reorder the terms: -40 + -42x + 4x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + -42x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -21x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -21x + 2x2)' equal to zero and attempt to solve: Simplifying -20 + -21x + 2x2 = 0 Solving -20 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10 + -10.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -10.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -10.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -10.5x + x2 = 0 + 10 -10.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -10.5x + x2 = 10 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 10 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 10 + 27.5625 Combine like terms: 10 + 27.5625 = 37.5625 27.5625 + -10.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -5.25) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -5.25 = 6.128825336 Simplifying x + -5.25 = 6.128825336 Reorder the terms: -5.25 + x = 6.128825336 Solving -5.25 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 6.128825336 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 6.128825336 + 5.25 x = 6.128825336 + 5.25 Combine like terms: 6.128825336 + 5.25 = 11.378825336 x = 11.378825336 Simplifying x = 11.378825336Subproblem 2
x + -5.25 = -6.128825336 Simplifying x + -5.25 = -6.128825336 Reorder the terms: -5.25 + x = -6.128825336 Solving -5.25 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -6.128825336 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -6.128825336 + 5.25 x = -6.128825336 + 5.25 Combine like terms: -6.128825336 + 5.25 = -0.878825336 x = -0.878825336 Simplifying x = -0.878825336Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.378825336, -0.878825336}Solution
x = {11.378825336, -0.878825336}
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