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Simplifying 11x2 + -3x + -5 = 0 Reorder the terms: -5 + -3x + 11x2 = 0 Solving -5 + -3x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.4545454545 + -0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + -0.2727272727x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + -0.2727272727x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + -0.2727272727x + x2 = 0 + 0.4545454545 -0.2727272727x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 -0.2727272727x + x2 = 0.4545454545 The x term is -0.2727272727x. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727x + 0.01859504133 + x2 = 0.4545454545 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727x + x2 = 0.4545454545 + 0.01859504133 Combine like terms: 0.4545454545 + 0.01859504133 = 0.47314049583 0.01859504133 + -0.2727272727x + x2 = 0.47314049583 Factor a perfect square on the left side: (x + -0.1363636364)(x + -0.1363636364) = 0.47314049583 Calculate the square root of the right side: 0.687852089 Break this problem into two subproblems by setting (x + -0.1363636364) equal to 0.687852089 and -0.687852089.Subproblem 1
x + -0.1363636364 = 0.687852089 Simplifying x + -0.1363636364 = 0.687852089 Reorder the terms: -0.1363636364 + x = 0.687852089 Solving -0.1363636364 + x = 0.687852089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = 0.687852089 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = 0.687852089 + 0.1363636364 x = 0.687852089 + 0.1363636364 Combine like terms: 0.687852089 + 0.1363636364 = 0.8242157254 x = 0.8242157254 Simplifying x = 0.8242157254Subproblem 2
x + -0.1363636364 = -0.687852089 Simplifying x + -0.1363636364 = -0.687852089 Reorder the terms: -0.1363636364 + x = -0.687852089 Solving -0.1363636364 + x = -0.687852089 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = -0.687852089 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = -0.687852089 + 0.1363636364 x = -0.687852089 + 0.1363636364 Combine like terms: -0.687852089 + 0.1363636364 = -0.5514884526 x = -0.5514884526 Simplifying x = -0.5514884526Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8242157254, -0.5514884526}
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