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Simplifying -6x2 + 3x + 19 = 0 Reorder the terms: 19 + 3x + -6x2 = 0 Solving 19 + 3x + -6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -3.166666667 + -0.5x + x2 = 0 Move the constant term to the right: Add '3.166666667' to each side of the equation. -3.166666667 + -0.5x + 3.166666667 + x2 = 0 + 3.166666667 Reorder the terms: -3.166666667 + 3.166666667 + -0.5x + x2 = 0 + 3.166666667 Combine like terms: -3.166666667 + 3.166666667 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 3.166666667 -0.5x + x2 = 0 + 3.166666667 Combine like terms: 0 + 3.166666667 = 3.166666667 -0.5x + x2 = 3.166666667 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 3.166666667 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 3.166666667 + 0.0625 Combine like terms: 3.166666667 + 0.0625 = 3.229166667 0.0625 + -0.5x + x2 = 3.229166667 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 3.229166667 Calculate the square root of the right side: 1.796988221 Break this problem into two subproblems by setting (x + -0.25) equal to 1.796988221 and -1.796988221.Subproblem 1
x + -0.25 = 1.796988221 Simplifying x + -0.25 = 1.796988221 Reorder the terms: -0.25 + x = 1.796988221 Solving -0.25 + x = 1.796988221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.796988221 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.796988221 + 0.25 x = 1.796988221 + 0.25 Combine like terms: 1.796988221 + 0.25 = 2.046988221 x = 2.046988221 Simplifying x = 2.046988221Subproblem 2
x + -0.25 = -1.796988221 Simplifying x + -0.25 = -1.796988221 Reorder the terms: -0.25 + x = -1.796988221 Solving -0.25 + x = -1.796988221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.796988221 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.796988221 + 0.25 x = -1.796988221 + 0.25 Combine like terms: -1.796988221 + 0.25 = -1.546988221 x = -1.546988221 Simplifying x = -1.546988221Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.046988221, -1.546988221}
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