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Simplifying 49x2 + 4x + -8 = 7x Reorder the terms: -8 + 4x + 49x2 = 7x Solving -8 + 4x + 49x2 = 7x Solving for variable 'x'. Reorder the terms: -8 + 4x + -7x + 49x2 = 7x + -7x Combine like terms: 4x + -7x = -3x -8 + -3x + 49x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -8 + -3x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1632653061 + -0.0612244898x + x2 = 0 Move the constant term to the right: Add '0.1632653061' to each side of the equation. -0.1632653061 + -0.0612244898x + 0.1632653061 + x2 = 0 + 0.1632653061 Reorder the terms: -0.1632653061 + 0.1632653061 + -0.0612244898x + x2 = 0 + 0.1632653061 Combine like terms: -0.1632653061 + 0.1632653061 = 0.0000000000 0.0000000000 + -0.0612244898x + x2 = 0 + 0.1632653061 -0.0612244898x + x2 = 0 + 0.1632653061 Combine like terms: 0 + 0.1632653061 = 0.1632653061 -0.0612244898x + x2 = 0.1632653061 The x term is -0.0612244898x. Take half its coefficient (-0.0306122449). Square it (0.0009371095378) and add it to both sides. Add '0.0009371095378' to each side of the equation. -0.0612244898x + 0.0009371095378 + x2 = 0.1632653061 + 0.0009371095378 Reorder the terms: 0.0009371095378 + -0.0612244898x + x2 = 0.1632653061 + 0.0009371095378 Combine like terms: 0.1632653061 + 0.0009371095378 = 0.1642024156378 0.0009371095378 + -0.0612244898x + x2 = 0.1642024156378 Factor a perfect square on the left side: (x + -0.0306122449)(x + -0.0306122449) = 0.1642024156378 Calculate the square root of the right side: 0.405218972 Break this problem into two subproblems by setting (x + -0.0306122449) equal to 0.405218972 and -0.405218972.Subproblem 1
x + -0.0306122449 = 0.405218972 Simplifying x + -0.0306122449 = 0.405218972 Reorder the terms: -0.0306122449 + x = 0.405218972 Solving -0.0306122449 + x = 0.405218972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0306122449' to each side of the equation. -0.0306122449 + 0.0306122449 + x = 0.405218972 + 0.0306122449 Combine like terms: -0.0306122449 + 0.0306122449 = 0.0000000000 0.0000000000 + x = 0.405218972 + 0.0306122449 x = 0.405218972 + 0.0306122449 Combine like terms: 0.405218972 + 0.0306122449 = 0.4358312169 x = 0.4358312169 Simplifying x = 0.4358312169Subproblem 2
x + -0.0306122449 = -0.405218972 Simplifying x + -0.0306122449 = -0.405218972 Reorder the terms: -0.0306122449 + x = -0.405218972 Solving -0.0306122449 + x = -0.405218972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0306122449' to each side of the equation. -0.0306122449 + 0.0306122449 + x = -0.405218972 + 0.0306122449 Combine like terms: -0.0306122449 + 0.0306122449 = 0.0000000000 0.0000000000 + x = -0.405218972 + 0.0306122449 x = -0.405218972 + 0.0306122449 Combine like terms: -0.405218972 + 0.0306122449 = -0.3746067271 x = -0.3746067271 Simplifying x = -0.3746067271Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4358312169, -0.3746067271}
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