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Simplifying 4x2 + 42x + -120 = 0 Reorder the terms: -120 + 42x + 4x2 = 0 Solving -120 + 42x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-60 + 21x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-60 + 21x + 2x2)' equal to zero and attempt to solve: Simplifying -60 + 21x + 2x2 = 0 Solving -60 + 21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -30 + 10.5x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 10.5x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 10.5x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 10.5x + x2 = 0 + 30 10.5x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 10.5x + x2 = 30 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 = 30 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 30 + 27.5625 Combine like terms: 30 + 27.5625 = 57.5625 27.5625 + 10.5x + x2 = 57.5625 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 57.5625 Calculate the square root of the right side: 7.586995453 Break this problem into two subproblems by setting (x + 5.25) equal to 7.586995453 and -7.586995453.Subproblem 1
x + 5.25 = 7.586995453 Simplifying x + 5.25 = 7.586995453 Reorder the terms: 5.25 + x = 7.586995453 Solving 5.25 + x = 7.586995453 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 = 7.586995453 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 7.586995453 + -5.25 x = 7.586995453 + -5.25 Combine like terms: 7.586995453 + -5.25 = 2.336995453 x = 2.336995453 Simplifying x = 2.336995453Subproblem 2
x + 5.25 = -7.586995453 Simplifying x + 5.25 = -7.586995453 Reorder the terms: 5.25 + x = -7.586995453 Solving 5.25 + x = -7.586995453 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 = -7.586995453 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -7.586995453 + -5.25 x = -7.586995453 + -5.25 Combine like terms: -7.586995453 + -5.25 = -12.836995453 x = -12.836995453 Simplifying x = -12.836995453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.336995453, -12.836995453}Solution
x = {2.336995453, -12.836995453}
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