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Simplifying 4.9x2 + -1x + -135 = 0 Reorder the terms: -135 + -1x + 4.9x2 = 0 Solving -135 + -1x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -27.55102041 + -0.2040816327x + x2 = 0 Move the constant term to the right: Add '27.55102041' to each side of the equation. -27.55102041 + -0.2040816327x + 27.55102041 + x2 = 0 + 27.55102041 Reorder the terms: -27.55102041 + 27.55102041 + -0.2040816327x + x2 = 0 + 27.55102041 Combine like terms: -27.55102041 + 27.55102041 = 0.00000000 0.00000000 + -0.2040816327x + x2 = 0 + 27.55102041 -0.2040816327x + x2 = 0 + 27.55102041 Combine like terms: 0 + 27.55102041 = 27.55102041 -0.2040816327x + x2 = 27.55102041 The x term is -0.2040816327x. Take half its coefficient (-0.1020408164). Square it (0.01041232821) and add it to both sides. Add '0.01041232821' to each side of the equation. -0.2040816327x + 0.01041232821 + x2 = 27.55102041 + 0.01041232821 Reorder the terms: 0.01041232821 + -0.2040816327x + x2 = 27.55102041 + 0.01041232821 Combine like terms: 27.55102041 + 0.01041232821 = 27.56143273821 0.01041232821 + -0.2040816327x + x2 = 27.56143273821 Factor a perfect square on the left side: (x + -0.1020408164)(x + -0.1020408164) = 27.56143273821 Calculate the square root of the right side: 5.249898355 Break this problem into two subproblems by setting (x + -0.1020408164) equal to 5.249898355 and -5.249898355.Subproblem 1
x + -0.1020408164 = 5.249898355 Simplifying x + -0.1020408164 = 5.249898355 Reorder the terms: -0.1020408164 + x = 5.249898355 Solving -0.1020408164 + x = 5.249898355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1020408164' to each side of the equation. -0.1020408164 + 0.1020408164 + x = 5.249898355 + 0.1020408164 Combine like terms: -0.1020408164 + 0.1020408164 = 0.0000000000 0.0000000000 + x = 5.249898355 + 0.1020408164 x = 5.249898355 + 0.1020408164 Combine like terms: 5.249898355 + 0.1020408164 = 5.3519391714 x = 5.3519391714 Simplifying x = 5.3519391714Subproblem 2
x + -0.1020408164 = -5.249898355 Simplifying x + -0.1020408164 = -5.249898355 Reorder the terms: -0.1020408164 + x = -5.249898355 Solving -0.1020408164 + x = -5.249898355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1020408164' to each side of the equation. -0.1020408164 + 0.1020408164 + x = -5.249898355 + 0.1020408164 Combine like terms: -0.1020408164 + 0.1020408164 = 0.0000000000 0.0000000000 + x = -5.249898355 + 0.1020408164 x = -5.249898355 + 0.1020408164 Combine like terms: -5.249898355 + 0.1020408164 = -5.1478575386 x = -5.1478575386 Simplifying x = -5.1478575386Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3519391714, -5.1478575386}
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