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Simplifying 34x2 + -34x + 34x2 + -1 = 0 Reorder the terms: -1 + -34x + 34x2 + 34x2 = 0 Combine like terms: 34x2 + 34x2 = 68x2 -1 + -34x + 68x2 = 0 Solving -1 + -34x + 68x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 68 the coefficient of the squared term: Divide each side by '68'. -0.01470588235 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.01470588235' to each side of the equation. -0.01470588235 + -0.5x + 0.01470588235 + x2 = 0 + 0.01470588235 Reorder the terms: -0.01470588235 + 0.01470588235 + -0.5x + x2 = 0 + 0.01470588235 Combine like terms: -0.01470588235 + 0.01470588235 = 0.00000000000 0.00000000000 + -0.5x + x2 = 0 + 0.01470588235 -0.5x + x2 = 0 + 0.01470588235 Combine like terms: 0 + 0.01470588235 = 0.01470588235 -0.5x + x2 = 0.01470588235 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.01470588235 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.01470588235 + 0.0625 Combine like terms: 0.01470588235 + 0.0625 = 0.07720588235 0.0625 + -0.5x + x2 = 0.07720588235 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.07720588235 Calculate the square root of the right side: 0.277859465 Break this problem into two subproblems by setting (x + -0.25) equal to 0.277859465 and -0.277859465.Subproblem 1
x + -0.25 = 0.277859465 Simplifying x + -0.25 = 0.277859465 Reorder the terms: -0.25 + x = 0.277859465 Solving -0.25 + x = 0.277859465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.277859465 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.277859465 + 0.25 x = 0.277859465 + 0.25 Combine like terms: 0.277859465 + 0.25 = 0.527859465 x = 0.527859465 Simplifying x = 0.527859465Subproblem 2
x + -0.25 = -0.277859465 Simplifying x + -0.25 = -0.277859465 Reorder the terms: -0.25 + x = -0.277859465 Solving -0.25 + x = -0.277859465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.277859465 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.277859465 + 0.25 x = -0.277859465 + 0.25 Combine like terms: -0.277859465 + 0.25 = -0.027859465 x = -0.027859465 Simplifying x = -0.027859465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.527859465, -0.027859465}
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