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Simplifying 4x2 + x + 4 = 169 Reorder the terms: 4 + x + 4x2 = 169 Solving 4 + x + 4x2 = 169 Solving for variable 'x'. Reorder the terms: 4 + -169 + x + 4x2 = 169 + -169 Combine like terms: 4 + -169 = -165 -165 + x + 4x2 = 169 + -169 Combine like terms: 169 + -169 = 0 -165 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -41.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '41.25' to each side of the equation. -41.25 + 0.25x + 41.25 + x2 = 0 + 41.25 Reorder the terms: -41.25 + 41.25 + 0.25x + x2 = 0 + 41.25 Combine like terms: -41.25 + 41.25 = 0.00 0.00 + 0.25x + x2 = 0 + 41.25 0.25x + x2 = 0 + 41.25 Combine like terms: 0 + 41.25 = 41.25 0.25x + x2 = 41.25 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. 0.25x + 0.25 + x2 = 41.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 41.25 + 0.25 Combine like terms: 41.25 + 0.25 = 41.5 0.25 + 0.25x + x2 = 41.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 41.5 Calculate the square root of the right side: 6.442049363 Break this problem into two subproblems by setting (x + 0.5) equal to 6.442049363 and -6.442049363.Subproblem 1
x + 0.5 = 6.442049363 Simplifying x + 0.5 = 6.442049363 Reorder the terms: 0.5 + x = 6.442049363 Solving 0.5 + x = 6.442049363 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 = 6.442049363 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.442049363 + -0.5 x = 6.442049363 + -0.5 Combine like terms: 6.442049363 + -0.5 = 5.942049363 x = 5.942049363 Simplifying x = 5.942049363Subproblem 2
x + 0.5 = -6.442049363 Simplifying x + 0.5 = -6.442049363 Reorder the terms: 0.5 + x = -6.442049363 Solving 0.5 + x = -6.442049363 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 = -6.442049363 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.442049363 + -0.5 x = -6.442049363 + -0.5 Combine like terms: -6.442049363 + -0.5 = -6.942049363 x = -6.942049363 Simplifying x = -6.942049363Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.942049363, -6.942049363}
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