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Simplifying 4x2 + 12x = 242 Reorder the terms: 12x + 4x2 = 242 Solving 12x + 4x2 = 242 Solving for variable 'x'. Reorder the terms: -242 + 12x + 4x2 = 242 + -242 Combine like terms: 242 + -242 = 0 -242 + 12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-121 + 6x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-121 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying -121 + 6x + 2x2 = 0 Solving -121 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -60.5 + 3x + x2 = 0 Move the constant term to the right: Add '60.5' to each side of the equation. -60.5 + 3x + 60.5 + x2 = 0 + 60.5 Reorder the terms: -60.5 + 60.5 + 3x + x2 = 0 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + 3x + x2 = 0 + 60.5 3x + x2 = 0 + 60.5 Combine like terms: 0 + 60.5 = 60.5 3x + x2 = 60.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 60.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 60.5 + 2.25 Combine like terms: 60.5 + 2.25 = 62.75 2.25 + 3x + x2 = 62.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (x + 1.5) equal to 7.921489759 and -7.921489759.Subproblem 1
x + 1.5 = 7.921489759 Simplifying x + 1.5 = 7.921489759 Reorder the terms: 1.5 + x = 7.921489759 Solving 1.5 + x = 7.921489759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.921489759 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.921489759 + -1.5 x = 7.921489759 + -1.5 Combine like terms: 7.921489759 + -1.5 = 6.421489759 x = 6.421489759 Simplifying x = 6.421489759Subproblem 2
x + 1.5 = -7.921489759 Simplifying x + 1.5 = -7.921489759 Reorder the terms: 1.5 + x = -7.921489759 Solving 1.5 + x = -7.921489759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.921489759 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.921489759 + -1.5 x = -7.921489759 + -1.5 Combine like terms: -7.921489759 + -1.5 = -9.421489759 x = -9.421489759 Simplifying x = -9.421489759Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.421489759, -9.421489759}Solution
x = {6.421489759, -9.421489759}
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