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Simplifying 0 = -6x2 + 8x + 3 Reorder the terms: 0 = 3 + 8x + -6x2 Solving 0 = 3 + 8x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -8x + 6x2 = 3 + 8x + -6x2 + -3 + -8x + 6x2 Reorder the terms: -3 + -8x + 6x2 = 3 + -3 + 8x + -8x + -6x2 + 6x2 Combine like terms: 3 + -3 = 0 -3 + -8x + 6x2 = 0 + 8x + -8x + -6x2 + 6x2 -3 + -8x + 6x2 = 8x + -8x + -6x2 + 6x2 Combine like terms: 8x + -8x = 0 -3 + -8x + 6x2 = 0 + -6x2 + 6x2 -3 + -8x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -3 + -8x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.333333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.333333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.333333333x + x2 = 0 + 0.5 -1.333333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.333333333x + x2 = 0.5 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 0.5 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.5 + 0.4444444442 Combine like terms: 0.5 + 0.4444444442 = 0.9444444442 0.4444444442 + -1.333333333x + x2 = 0.9444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.9444444442 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.971825316 and -0.971825316.Subproblem 1
x + -0.6666666665 = 0.971825316 Simplifying x + -0.6666666665 = 0.971825316 Reorder the terms: -0.6666666665 + x = 0.971825316 Solving -0.6666666665 + x = 0.971825316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.971825316 + 0.6666666665 x = 0.971825316 + 0.6666666665 Combine like terms: 0.971825316 + 0.6666666665 = 1.6384919825 x = 1.6384919825 Simplifying x = 1.6384919825Subproblem 2
x + -0.6666666665 = -0.971825316 Simplifying x + -0.6666666665 = -0.971825316 Reorder the terms: -0.6666666665 + x = -0.971825316 Solving -0.6666666665 + x = -0.971825316 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -0.971825316 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.971825316 + 0.6666666665 x = -0.971825316 + 0.6666666665 Combine like terms: -0.971825316 + 0.6666666665 = -0.3051586495 x = -0.3051586495 Simplifying x = -0.3051586495Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6384919825, -0.3051586495}
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