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Simplifying -1(5x2 + 11x + 5) = 0 Reorder the terms: -1(5 + 11x + 5x2) = 0 (5 * -1 + 11x * -1 + 5x2 * -1) = 0 (-5 + -11x + -5x2) = 0 Solving -5 + -11x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 11x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 11x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + 11x + 5x2 = 0 Solving 5 + 11x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 2.2x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.2x + x2 = 0 + -1 2.2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.2x + x2 = -1 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 = -1 + 1.21 Reorder the terms: 1.21 + 2.2x + x2 = -1 + 1.21 Combine like terms: -1 + 1.21 = 0.21 1.21 + 2.2x + x2 = 0.21 Factor a perfect square on the left side: (x + 1.1)(x + 1.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + 1.1) equal to 0.458257569 and -0.458257569.Subproblem 1
x + 1.1 = 0.458257569 Simplifying x + 1.1 = 0.458257569 Reorder the terms: 1.1 + x = 0.458257569 Solving 1.1 + x = 0.458257569 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 = 0.458257569 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = 0.458257569 + -1.1 x = 0.458257569 + -1.1 Combine like terms: 0.458257569 + -1.1 = -0.641742431 x = -0.641742431 Simplifying x = -0.641742431Subproblem 2
x + 1.1 = -0.458257569 Simplifying x + 1.1 = -0.458257569 Reorder the terms: 1.1 + x = -0.458257569 Solving 1.1 + x = -0.458257569 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 = -0.458257569 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + x = -0.458257569 + -1.1 x = -0.458257569 + -1.1 Combine like terms: -0.458257569 + -1.1 = -1.558257569 x = -1.558257569 Simplifying x = -1.558257569Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.641742431, -1.558257569}Solution
x = {-0.641742431, -1.558257569}
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