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Simplifying 0 = 5x2 + 11x + 1 Reorder the terms: 0 = 1 + 11x + 5x2 Solving 0 = 1 + 11x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + -11x + -5x2 = 1 + 11x + 5x2 + -1 + -11x + -5x2 Reorder the terms: -1 + -11x + -5x2 = 1 + -1 + 11x + -11x + 5x2 + -5x2 Combine like terms: 1 + -1 = 0 -1 + -11x + -5x2 = 0 + 11x + -11x + 5x2 + -5x2 -1 + -11x + -5x2 = 11x + -11x + 5x2 + -5x2 Combine like terms: 11x + -11x = 0 -1 + -11x + -5x2 = 0 + 5x2 + -5x2 -1 + -11x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -1 + -11x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 11x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 11x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + 11x + 5x2 = 0 Solving 1 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2.2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2.2x + x2 = 0 + -0.2 2.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2.2x + x2 = -0.2 The x term is 2.2x. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2x + 1.21 + x2 = -0.2 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = -0.2 + 1.21 Combine like terms: -0.2 + 1.21 = 1.01 1.21 + 2.2x + x2 = 1.01 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + 1.1) equal to 1.004987562 and -1.004987562.Subproblem 1
x + 1.1 = 1.004987562 Simplifying x + 1.1 = 1.004987562 Reorder the terms: 1.1 + x = 1.004987562 Solving 1.1 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = 1.004987562 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 1.004987562 + -1.1 x = 1.004987562 + -1.1 Combine like terms: 1.004987562 + -1.1 = -0.095012438 x = -0.095012438 Simplifying x = -0.095012438Subproblem 2
x + 1.1 = -1.004987562 Simplifying x + 1.1 = -1.004987562 Reorder the terms: 1.1 + x = -1.004987562 Solving 1.1 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + x = -1.004987562 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -1.004987562 + -1.1 x = -1.004987562 + -1.1 Combine like terms: -1.004987562 + -1.1 = -2.104987562 x = -2.104987562 Simplifying x = -2.104987562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.095012438, -2.104987562}Solution
x = {-0.095012438, -2.104987562}
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