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Simplifying 9x2 = 18 + -5x Solving 9x2 = 18 + -5x Solving for variable 'x'. Reorder the terms: -18 + 5x + 9x2 = 18 + -5x + -18 + 5x Reorder the terms: -18 + 5x + 9x2 = 18 + -18 + -5x + 5x Combine like terms: 18 + -18 = 0 -18 + 5x + 9x2 = 0 + -5x + 5x -18 + 5x + 9x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -18 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5555555556x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5555555556x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5555555556x + x2 = 0 + 2 0.5555555556x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5555555556x + x2 = 2 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 = 2 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 2 + 0.07716049384 Combine like terms: 2 + 0.07716049384 = 2.07716049384 0.07716049384 + 0.5555555556x + x2 = 2.07716049384 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 2.07716049384 Calculate the square root of the right side: 1.441235752 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 1.441235752 and -1.441235752.Subproblem 1
x + 0.2777777778 = 1.441235752 Simplifying x + 0.2777777778 = 1.441235752 Reorder the terms: 0.2777777778 + x = 1.441235752 Solving 0.2777777778 + x = 1.441235752 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 = 1.441235752 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 1.441235752 + -0.2777777778 x = 1.441235752 + -0.2777777778 Combine like terms: 1.441235752 + -0.2777777778 = 1.1634579742 x = 1.1634579742 Simplifying x = 1.1634579742Subproblem 2
x + 0.2777777778 = -1.441235752 Simplifying x + 0.2777777778 = -1.441235752 Reorder the terms: 0.2777777778 + x = -1.441235752 Solving 0.2777777778 + x = -1.441235752 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 = -1.441235752 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -1.441235752 + -0.2777777778 x = -1.441235752 + -0.2777777778 Combine like terms: -1.441235752 + -0.2777777778 = -1.7190135298 x = -1.7190135298 Simplifying x = -1.7190135298Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1634579742, -1.7190135298}
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