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Simplifying 116 = 4x(2x + 6) Reorder the terms: 116 = 4x(6 + 2x) 116 = (6 * 4x + 2x * 4x) 116 = (24x + 8x2) Solving 116 = 24x + 8x2 Solving for variable 'x'. Reorder the terms: 116 + -24x + -8x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 116 + -24x + -8x2 = 0 + 8x2 + -8x2 116 + -24x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 116 + -24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(29 + -6x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(29 + -6x + -2x2)' equal to zero and attempt to solve: Simplifying 29 + -6x + -2x2 = 0 Solving 29 + -6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -14.5 + 3x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + 3x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + 3x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + 3x + x2 = 0 + 14.5 3x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 3x + x2 = 14.5 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 = 14.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 14.5 + 2.25 Combine like terms: 14.5 + 2.25 = 16.75 2.25 + 3x + x2 = 16.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 16.75 Calculate the square root of the right side: 4.092676386 Break this problem into two subproblems by setting (x + 1.5) equal to 4.092676386 and -4.092676386.Subproblem 1
x + 1.5 = 4.092676386 Simplifying x + 1.5 = 4.092676386 Reorder the terms: 1.5 + x = 4.092676386 Solving 1.5 + x = 4.092676386 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 = 4.092676386 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 4.092676386 + -1.5 x = 4.092676386 + -1.5 Combine like terms: 4.092676386 + -1.5 = 2.592676386 x = 2.592676386 Simplifying x = 2.592676386Subproblem 2
x + 1.5 = -4.092676386 Simplifying x + 1.5 = -4.092676386 Reorder the terms: 1.5 + x = -4.092676386 Solving 1.5 + x = -4.092676386 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 = -4.092676386 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -4.092676386 + -1.5 x = -4.092676386 + -1.5 Combine like terms: -4.092676386 + -1.5 = -5.592676386 x = -5.592676386 Simplifying x = -5.592676386Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.592676386, -5.592676386}Solution
x = {2.592676386, -5.592676386}
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