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Simplifying 16x2 + 31x + -3 = 0 Reorder the terms: -3 + 31x + 16x2 = 0 Solving -3 + 31x + 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'. -0.1875 + 1.9375x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 1.9375x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 1.9375x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 1.9375x + x2 = 0 + 0.1875 1.9375x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 1.9375x + x2 = 0.1875 The x term is 1.9375x. Take half its coefficient (0.96875). Square it (0.9384765625) and add it to both sides. Add '0.9384765625' to each side of the equation. 1.9375x + 0.9384765625 + x2 = 0.1875 + 0.9384765625 Reorder the terms: 0.9384765625 + 1.9375x + x2 = 0.1875 + 0.9384765625 Combine like terms: 0.1875 + 0.9384765625 = 1.1259765625 0.9384765625 + 1.9375x + x2 = 1.1259765625 Factor a perfect square on the left side: (x + 0.96875)(x + 0.96875) = 1.1259765625 Calculate the square root of the right side: 1.061120428 Break this problem into two subproblems by setting (x + 0.96875) equal to 1.061120428 and -1.061120428.Subproblem 1
x + 0.96875 = 1.061120428 Simplifying x + 0.96875 = 1.061120428 Reorder the terms: 0.96875 + x = 1.061120428 Solving 0.96875 + x = 1.061120428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + x = 1.061120428 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = 1.061120428 + -0.96875 x = 1.061120428 + -0.96875 Combine like terms: 1.061120428 + -0.96875 = 0.092370428 x = 0.092370428 Simplifying x = 0.092370428Subproblem 2
x + 0.96875 = -1.061120428 Simplifying x + 0.96875 = -1.061120428 Reorder the terms: 0.96875 + x = -1.061120428 Solving 0.96875 + x = -1.061120428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.96875' to each side of the equation. 0.96875 + -0.96875 + x = -1.061120428 + -0.96875 Combine like terms: 0.96875 + -0.96875 = 0.00000 0.00000 + x = -1.061120428 + -0.96875 x = -1.061120428 + -0.96875 Combine like terms: -1.061120428 + -0.96875 = -2.029870428 x = -2.029870428 Simplifying x = -2.029870428Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.092370428, -2.029870428}
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