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Simplifying -6x2 + -9x + 1 = 0 Reorder the terms: 1 + -9x + -6x2 = 0 Solving 1 + -9x + -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'. -0.1666666667 + 1.5x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + 1.5x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + 1.5x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + 1.5x + x2 = 0 + 0.1666666667 1.5x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 1.5x + x2 = 0.1666666667 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 0.1666666667 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 0.1666666667 + 0.5625 Combine like terms: 0.1666666667 + 0.5625 = 0.7291666667 0.5625 + 1.5x + x2 = 0.7291666667 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 0.7291666667 Calculate the square root of the right side: 0.853912564 Break this problem into two subproblems by setting (x + 0.75) equal to 0.853912564 and -0.853912564.Subproblem 1
x + 0.75 = 0.853912564 Simplifying x + 0.75 = 0.853912564 Reorder the terms: 0.75 + x = 0.853912564 Solving 0.75 + x = 0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 0.853912564 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 0.853912564 + -0.75 x = 0.853912564 + -0.75 Combine like terms: 0.853912564 + -0.75 = 0.103912564 x = 0.103912564 Simplifying x = 0.103912564Subproblem 2
x + 0.75 = -0.853912564 Simplifying x + 0.75 = -0.853912564 Reorder the terms: 0.75 + x = -0.853912564 Solving 0.75 + x = -0.853912564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -0.853912564 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -0.853912564 + -0.75 x = -0.853912564 + -0.75 Combine like terms: -0.853912564 + -0.75 = -1.603912564 x = -1.603912564 Simplifying x = -1.603912564Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.103912564, -1.603912564}
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