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Simplifying 9x2 + -5x + -3 = 0 Reorder the terms: -3 + -5x + 9x2 = 0 Solving -3 + -5x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.5555555556x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.5555555556x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.5555555556x + x2 = 0 + 0.3333333333 -0.5555555556x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.5555555556x + x2 = 0.3333333333 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 0.3333333333 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 0.3333333333 + 0.07716049384 Combine like terms: 0.3333333333 + 0.07716049384 = 0.41049382714 0.07716049384 + -0.5555555556x + x2 = 0.41049382714 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 0.41049382714 Calculate the square root of the right side: 0.640697922 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 0.640697922 and -0.640697922.Subproblem 1
x + -0.2777777778 = 0.640697922 Simplifying x + -0.2777777778 = 0.640697922 Reorder the terms: -0.2777777778 + x = 0.640697922 Solving -0.2777777778 + x = 0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 0.640697922 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 0.640697922 + 0.2777777778 x = 0.640697922 + 0.2777777778 Combine like terms: 0.640697922 + 0.2777777778 = 0.9184756998 x = 0.9184756998 Simplifying x = 0.9184756998Subproblem 2
x + -0.2777777778 = -0.640697922 Simplifying x + -0.2777777778 = -0.640697922 Reorder the terms: -0.2777777778 + x = -0.640697922 Solving -0.2777777778 + x = -0.640697922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -0.640697922 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -0.640697922 + 0.2777777778 x = -0.640697922 + 0.2777777778 Combine like terms: -0.640697922 + 0.2777777778 = -0.3629201442 x = -0.3629201442 Simplifying x = -0.3629201442Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9184756998, -0.3629201442}
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