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Simplifying 350 = 24x2 + 24x + -6 Reorder the terms: 350 = -6 + 24x + 24x2 Solving 350 = -6 + 24x + 24x2 Solving for variable 'x'. Combine like terms: 350 + 6 = 356 356 + -24x + -24x2 = -6 + 24x + 24x2 + 6 + -24x + -24x2 Reorder the terms: 356 + -24x + -24x2 = -6 + 6 + 24x + -24x + 24x2 + -24x2 Combine like terms: -6 + 6 = 0 356 + -24x + -24x2 = 0 + 24x + -24x + 24x2 + -24x2 356 + -24x + -24x2 = 24x + -24x + 24x2 + -24x2 Combine like terms: 24x + -24x = 0 356 + -24x + -24x2 = 0 + 24x2 + -24x2 356 + -24x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 356 + -24x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(89 + -6x + -6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(89 + -6x + -6x2)' equal to zero and attempt to solve: Simplifying 89 + -6x + -6x2 = 0 Solving 89 + -6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -14.83333333 + x + x2 = 0 Move the constant term to the right: Add '14.83333333' to each side of the equation. -14.83333333 + x + 14.83333333 + x2 = 0 + 14.83333333 Reorder the terms: -14.83333333 + 14.83333333 + x + x2 = 0 + 14.83333333 Combine like terms: -14.83333333 + 14.83333333 = 0.00000000 0.00000000 + x + x2 = 0 + 14.83333333 x + x2 = 0 + 14.83333333 Combine like terms: 0 + 14.83333333 = 14.83333333 x + x2 = 14.83333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 14.83333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 14.83333333 + 0.25 Combine like terms: 14.83333333 + 0.25 = 15.08333333 1.25 + x2 = 15.08333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 15.08333333 Calculate the square root of the right side: 3.883726732 Break this problem into two subproblems by setting (x + 0.5) equal to 3.883726732 and -3.883726732.Subproblem 1
x + 0.5 = 3.883726732 Simplifying x + 0.5 = 3.883726732 Reorder the terms: 0.5 + x = 3.883726732 Solving 0.5 + x = 3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.883726732 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.883726732 + -0.5 x = 3.883726732 + -0.5 Combine like terms: 3.883726732 + -0.5 = 3.383726732 x = 3.383726732 Simplifying x = 3.383726732Subproblem 2
x + 0.5 = -3.883726732 Simplifying x + 0.5 = -3.883726732 Reorder the terms: 0.5 + x = -3.883726732 Solving 0.5 + x = -3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.883726732 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.883726732 + -0.5 x = -3.883726732 + -0.5 Combine like terms: -3.883726732 + -0.5 = -4.383726732 x = -4.383726732 Simplifying x = -4.383726732Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.383726732, -4.383726732}Solution
x = {3.383726732, -4.383726732}
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