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Simplifying 6x2 + 5x2 + -3x + -2 = 0 Reorder the terms: -2 + -3x + 6x2 + 5x2 = 0 Combine like terms: 6x2 + 5x2 = 11x2 -2 + -3x + 11x2 = 0 Solving -2 + -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'. -0.1818181818 + -0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.2727272727x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.2727272727x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.2727272727x + x2 = 0 + 0.1818181818 -0.2727272727x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.2727272727x + x2 = 0.1818181818 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 = 0.1818181818 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727x + x2 = 0.1818181818 + 0.01859504133 Combine like terms: 0.1818181818 + 0.01859504133 = 0.20041322313 0.01859504133 + -0.2727272727x + x2 = 0.20041322313 Factor a perfect square on the left side: (x + -0.1363636364)(x + -0.1363636364) = 0.20041322313 Calculate the square root of the right side: 0.447675355 Break this problem into two subproblems by setting (x + -0.1363636364) equal to 0.447675355 and -0.447675355.Subproblem 1
x + -0.1363636364 = 0.447675355 Simplifying x + -0.1363636364 = 0.447675355 Reorder the terms: -0.1363636364 + x = 0.447675355 Solving -0.1363636364 + x = 0.447675355 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 = 0.447675355 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = 0.447675355 + 0.1363636364 x = 0.447675355 + 0.1363636364 Combine like terms: 0.447675355 + 0.1363636364 = 0.5840389914 x = 0.5840389914 Simplifying x = 0.5840389914Subproblem 2
x + -0.1363636364 = -0.447675355 Simplifying x + -0.1363636364 = -0.447675355 Reorder the terms: -0.1363636364 + x = -0.447675355 Solving -0.1363636364 + x = -0.447675355 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 = -0.447675355 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = -0.447675355 + 0.1363636364 x = -0.447675355 + 0.1363636364 Combine like terms: -0.447675355 + 0.1363636364 = -0.3113117186 x = -0.3113117186 Simplifying x = -0.3113117186Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5840389914, -0.3113117186}
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