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Simplifying 16x2 + 9x + -30 = 0 Reorder the terms: -30 + 9x + 16x2 = 0 Solving -30 + 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'. -1.875 + 0.5625x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 0.5625x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 0.5625x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 0.5625x + x2 = 0 + 1.875 0.5625x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 0.5625x + x2 = 1.875 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 = 1.875 + 0.0791015625 Reorder the terms: 0.0791015625 + 0.5625x + x2 = 1.875 + 0.0791015625 Combine like terms: 1.875 + 0.0791015625 = 1.9541015625 0.0791015625 + 0.5625x + x2 = 1.9541015625 Factor a perfect square on the left side: (x + 0.28125)(x + 0.28125) = 1.9541015625 Calculate the square root of the right side: 1.397891828 Break this problem into two subproblems by setting (x + 0.28125) equal to 1.397891828 and -1.397891828.Subproblem 1
x + 0.28125 = 1.397891828 Simplifying x + 0.28125 = 1.397891828 Reorder the terms: 0.28125 + x = 1.397891828 Solving 0.28125 + x = 1.397891828 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 = 1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = 1.397891828 + -0.28125 x = 1.397891828 + -0.28125 Combine like terms: 1.397891828 + -0.28125 = 1.116641828 x = 1.116641828 Simplifying x = 1.116641828Subproblem 2
x + 0.28125 = -1.397891828 Simplifying x + 0.28125 = -1.397891828 Reorder the terms: 0.28125 + x = -1.397891828 Solving 0.28125 + x = -1.397891828 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 = -1.397891828 + -0.28125 Combine like terms: 0.28125 + -0.28125 = 0.00000 0.00000 + x = -1.397891828 + -0.28125 x = -1.397891828 + -0.28125 Combine like terms: -1.397891828 + -0.28125 = -1.679141828 x = -1.679141828 Simplifying x = -1.679141828Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.116641828, -1.679141828}
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