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Simplifying 2x + 19 = 64x2 Reorder the terms: 19 + 2x = 64x2 Solving 19 + 2x = 64x2 Solving for variable 'x'. Combine like terms: 64x2 + -64x2 = 0 19 + 2x + -64x2 = 0 Begin completing the square. Divide all terms by -64 the coefficient of the squared term: Divide each side by '-64'. -0.296875 + -0.03125x + x2 = 0 Move the constant term to the right: Add '0.296875' to each side of the equation. -0.296875 + -0.03125x + 0.296875 + x2 = 0 + 0.296875 Reorder the terms: -0.296875 + 0.296875 + -0.03125x + x2 = 0 + 0.296875 Combine like terms: -0.296875 + 0.296875 = 0.000000 0.000000 + -0.03125x + x2 = 0 + 0.296875 -0.03125x + x2 = 0 + 0.296875 Combine like terms: 0 + 0.296875 = 0.296875 -0.03125x + x2 = 0.296875 The x term is -0.03125x. Take half its coefficient (-0.015625). Square it (0.000244140625) and add it to both sides. Add '0.000244140625' to each side of the equation. -0.03125x + 0.000244140625 + x2 = 0.296875 + 0.000244140625 Reorder the terms: 0.000244140625 + -0.03125x + x2 = 0.296875 + 0.000244140625 Combine like terms: 0.296875 + 0.000244140625 = 0.297119140625 0.000244140625 + -0.03125x + x2 = 0.297119140625 Factor a perfect square on the left side: (x + -0.015625)(x + -0.015625) = 0.297119140625 Calculate the square root of the right side: 0.545086361 Break this problem into two subproblems by setting (x + -0.015625) equal to 0.545086361 and -0.545086361.Subproblem 1
x + -0.015625 = 0.545086361 Simplifying x + -0.015625 = 0.545086361 Reorder the terms: -0.015625 + x = 0.545086361 Solving -0.015625 + x = 0.545086361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = 0.545086361 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = 0.545086361 + 0.015625 x = 0.545086361 + 0.015625 Combine like terms: 0.545086361 + 0.015625 = 0.560711361 x = 0.560711361 Simplifying x = 0.560711361Subproblem 2
x + -0.015625 = -0.545086361 Simplifying x + -0.015625 = -0.545086361 Reorder the terms: -0.015625 + x = -0.545086361 Solving -0.015625 + x = -0.545086361 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.015625' to each side of the equation. -0.015625 + 0.015625 + x = -0.545086361 + 0.015625 Combine like terms: -0.015625 + 0.015625 = 0.000000 0.000000 + x = -0.545086361 + 0.015625 x = -0.545086361 + 0.015625 Combine like terms: -0.545086361 + 0.015625 = -0.529461361 x = -0.529461361 Simplifying x = -0.529461361Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.560711361, -0.529461361}
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