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Simplifying 9x2 + 10x2 + -4x + -9 + 29x2 + 5 + 14x + -8x = 0 Reorder the terms: -9 + 5 + -4x + 14x + -8x + 9x2 + 10x2 + 29x2 = 0 Combine like terms: -9 + 5 = -4 -4 + -4x + 14x + -8x + 9x2 + 10x2 + 29x2 = 0 Combine like terms: -4x + 14x = 10x -4 + 10x + -8x + 9x2 + 10x2 + 29x2 = 0 Combine like terms: 10x + -8x = 2x -4 + 2x + 9x2 + 10x2 + 29x2 = 0 Combine like terms: 9x2 + 10x2 = 19x2 -4 + 2x + 19x2 + 29x2 = 0 Combine like terms: 19x2 + 29x2 = 48x2 -4 + 2x + 48x2 = 0 Solving -4 + 2x + 48x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x + 24x2)' equal to zero and attempt to solve: Simplifying -2 + x + 24x2 = 0 Solving -2 + x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.08333333333 + 0.04166666667x + x2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.04166666667x + 0.08333333333 + x2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.04166666667x + x2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.04166666667x + x2 = 0 + 0.08333333333 0.04166666667x + x2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.04166666667x + x2 = 0.08333333333 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. 0.04166666667x + 0.25 + x2 = 0.08333333333 + 0.25 Reorder the terms: 0.25 + 0.04166666667x + x2 = 0.08333333333 + 0.25 Combine like terms: 0.08333333333 + 0.25 = 0.33333333333 0.25 + 0.04166666667x + x2 = 0.33333333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.33333333333 Calculate the square root of the right side: 0.577350269 Break this problem into two subproblems by setting (x + 0.5) equal to 0.577350269 and -0.577350269.Subproblem 1
x + 0.5 = 0.577350269 Simplifying x + 0.5 = 0.577350269 Reorder the terms: 0.5 + x = 0.577350269 Solving 0.5 + x = 0.577350269 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 = 0.577350269 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.577350269 + -0.5 x = 0.577350269 + -0.5 Combine like terms: 0.577350269 + -0.5 = 0.077350269 x = 0.077350269 Simplifying x = 0.077350269Subproblem 2
x + 0.5 = -0.577350269 Simplifying x + 0.5 = -0.577350269 Reorder the terms: 0.5 + x = -0.577350269 Solving 0.5 + x = -0.577350269 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 = -0.577350269 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.577350269 + -0.5 x = -0.577350269 + -0.5 Combine like terms: -0.577350269 + -0.5 = -1.077350269 x = -1.077350269 Simplifying x = -1.077350269Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.077350269, -1.077350269}Solution
x = {0.077350269, -1.077350269}
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