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Simplifying 4x2 + 8x = 162 Reorder the terms: 8x + 4x2 = 162 Solving 8x + 4x2 = 162 Solving for variable 'x'. Reorder the terms: -162 + 8x + 4x2 = 162 + -162 Combine like terms: 162 + -162 = 0 -162 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-81 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-81 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -81 + 4x + 2x2 = 0 Solving -81 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40.5 + 2x + x2 = 0 Move the constant term to the right: Add '40.5' to each side of the equation. -40.5 + 2x + 40.5 + x2 = 0 + 40.5 Reorder the terms: -40.5 + 40.5 + 2x + x2 = 0 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + 2x + x2 = 0 + 40.5 2x + x2 = 0 + 40.5 Combine like terms: 0 + 40.5 = 40.5 2x + x2 = 40.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 40.5 + 1 Reorder the terms: 1 + 2x + x2 = 40.5 + 1 Combine like terms: 40.5 + 1 = 41.5 1 + 2x + x2 = 41.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 41.5 Calculate the square root of the right side: 6.442049363 Break this problem into two subproblems by setting (x + 1) equal to 6.442049363 and -6.442049363.Subproblem 1
x + 1 = 6.442049363 Simplifying x + 1 = 6.442049363 Reorder the terms: 1 + x = 6.442049363 Solving 1 + x = 6.442049363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.442049363 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.442049363 + -1 x = 6.442049363 + -1 Combine like terms: 6.442049363 + -1 = 5.442049363 x = 5.442049363 Simplifying x = 5.442049363Subproblem 2
x + 1 = -6.442049363 Simplifying x + 1 = -6.442049363 Reorder the terms: 1 + x = -6.442049363 Solving 1 + x = -6.442049363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.442049363 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.442049363 + -1 x = -6.442049363 + -1 Combine like terms: -6.442049363 + -1 = -7.442049363 x = -7.442049363 Simplifying x = -7.442049363Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.442049363, -7.442049363}Solution
x = {5.442049363, -7.442049363}
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