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Simplifying -16x2 + 71x + 6 = 0 Reorder the terms: 6 + 71x + -16x2 = 0 Solving 6 + 71x + -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'. -0.375 + -4.4375x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -4.4375x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -4.4375x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -4.4375x + x2 = 0 + 0.375 -4.4375x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -4.4375x + x2 = 0.375 The x term is -4.4375x. Take half its coefficient (-2.21875). Square it (4.922851563) and add it to both sides. Add '4.922851563' to each side of the equation. -4.4375x + 4.922851563 + x2 = 0.375 + 4.922851563 Reorder the terms: 4.922851563 + -4.4375x + x2 = 0.375 + 4.922851563 Combine like terms: 0.375 + 4.922851563 = 5.297851563 4.922851563 + -4.4375x + x2 = 5.297851563 Factor a perfect square on the left side: (x + -2.21875)(x + -2.21875) = 5.297851563 Calculate the square root of the right side: 2.301706229 Break this problem into two subproblems by setting (x + -2.21875) equal to 2.301706229 and -2.301706229.Subproblem 1
x + -2.21875 = 2.301706229 Simplifying x + -2.21875 = 2.301706229 Reorder the terms: -2.21875 + x = 2.301706229 Solving -2.21875 + x = 2.301706229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.21875' to each side of the equation. -2.21875 + 2.21875 + x = 2.301706229 + 2.21875 Combine like terms: -2.21875 + 2.21875 = 0.00000 0.00000 + x = 2.301706229 + 2.21875 x = 2.301706229 + 2.21875 Combine like terms: 2.301706229 + 2.21875 = 4.520456229 x = 4.520456229 Simplifying x = 4.520456229Subproblem 2
x + -2.21875 = -2.301706229 Simplifying x + -2.21875 = -2.301706229 Reorder the terms: -2.21875 + x = -2.301706229 Solving -2.21875 + x = -2.301706229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.21875' to each side of the equation. -2.21875 + 2.21875 + x = -2.301706229 + 2.21875 Combine like terms: -2.21875 + 2.21875 = 0.00000 0.00000 + x = -2.301706229 + 2.21875 x = -2.301706229 + 2.21875 Combine like terms: -2.301706229 + 2.21875 = -0.082956229 x = -0.082956229 Simplifying x = -0.082956229Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.520456229, -0.082956229}
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