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Simplifying 8x2 + 36x + -16 = 0 Reorder the terms: -16 + 36x + 8x2 = 0 Solving -16 + 36x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + 9x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + 9x + 2x2)' equal to zero and attempt to solve: Simplifying -4 + 9x + 2x2 = 0 Solving -4 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2 + 4.5x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.5x + x2 = 0 + 2 4.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.5x + x2 = 2 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 2 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 2 + 5.0625 Combine like terms: 2 + 5.0625 = 7.0625 5.0625 + 4.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + 2.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + 2.25 = 2.657536453 Simplifying x + 2.25 = 2.657536453 Reorder the terms: 2.25 + x = 2.657536453 Solving 2.25 + x = 2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 2.657536453 + -2.25 x = 2.657536453 + -2.25 Combine like terms: 2.657536453 + -2.25 = 0.407536453 x = 0.407536453 Simplifying x = 0.407536453Subproblem 2
x + 2.25 = -2.657536453 Simplifying x + 2.25 = -2.657536453 Reorder the terms: 2.25 + x = -2.657536453 Solving 2.25 + x = -2.657536453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -2.657536453 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -2.657536453 + -2.25 x = -2.657536453 + -2.25 Combine like terms: -2.657536453 + -2.25 = -4.907536453 x = -4.907536453 Simplifying x = -4.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.407536453, -4.907536453}Solution
x = {0.407536453, -4.907536453}
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