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Simplifying 36x2 + -20x2 + 9x + -5 = 0 Reorder the terms: -5 + 9x + 36x2 + -20x2 = 0 Combine like terms: 36x2 + -20x2 = 16x2 -5 + 9x + 16x2 = 0 Solving -5 + 9x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + 0.5625x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.5625x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.5625x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.5625x + x2 = 0 + 0.3125 0.5625x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 0.5625x + x2 = 0.3125 The x term is 0.5625x. Take half its coefficient (0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. 0.5625x + 0.0791015625 + x2 = 0.3125 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 0.3125 + 0.0791015625 Combine like terms: 0.3125 + 0.0791015625 = 0.3916015625 0.0791015625 + 0.5625x + x2 = 0.3916015625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 0.3916015625 Calculate the square root of the right side: 0.625780762 Break this problem into two subproblems by setting (x + 0.28125) equal to 0.625780762 and -0.625780762.Subproblem 1
x + 0.28125 = 0.625780762 Simplifying x + 0.28125 = 0.625780762 Reorder the terms: 0.28125 + x = 0.625780762 Solving 0.28125 + x = 0.625780762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = 0.625780762 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 0.625780762 + -0.28125 x = 0.625780762 + -0.28125 Combine like terms: 0.625780762 + -0.28125 = 0.344530762 x = 0.344530762 Simplifying x = 0.344530762Subproblem 2
x + 0.28125 = -0.625780762 Simplifying x + 0.28125 = -0.625780762 Reorder the terms: 0.28125 + x = -0.625780762 Solving 0.28125 + x = -0.625780762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.28125' to each side of the equation. 0.28125 + -0.28125 + x = -0.625780762 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -0.625780762 + -0.28125 x = -0.625780762 + -0.28125 Combine like terms: -0.625780762 + -0.28125 = -0.907030762 x = -0.907030762 Simplifying x = -0.907030762Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.344530762, -0.907030762}
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