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Simplifying 9x2 + -5x = 16 + -4x Reorder the terms: -5x + 9x2 = 16 + -4x Solving -5x + 9x2 = 16 + -4x Solving for variable 'x'. Reorder the terms: -16 + -5x + 4x + 9x2 = 16 + -4x + -16 + 4x Combine like terms: -5x + 4x = -1x -16 + -1x + 9x2 = 16 + -4x + -16 + 4x Reorder the terms: -16 + -1x + 9x2 = 16 + -16 + -4x + 4x Combine like terms: 16 + -16 = 0 -16 + -1x + 9x2 = 0 + -4x + 4x -16 + -1x + 9x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -16 + -1x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + -0.1111111111x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + -0.1111111111x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 1.777777778 -0.1111111111x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 -0.1111111111x + x2 = 1.777777778 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 1.777777778 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 1.777777778 + 0.003086419752 Combine like terms: 1.777777778 + 0.003086419752 = 1.780864197752 0.003086419752 + -0.1111111111x + x2 = 1.780864197752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 1.780864197752 Calculate the square root of the right side: 1.334490239 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.334490239 and -1.334490239.Subproblem 1
x + -0.05555555555 = 1.334490239 Simplifying x + -0.05555555555 = 1.334490239 Reorder the terms: -0.05555555555 + x = 1.334490239 Solving -0.05555555555 + x = 1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.334490239 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.334490239 + 0.05555555555 x = 1.334490239 + 0.05555555555 Combine like terms: 1.334490239 + 0.05555555555 = 1.39004579455 x = 1.39004579455 Simplifying x = 1.39004579455Subproblem 2
x + -0.05555555555 = -1.334490239 Simplifying x + -0.05555555555 = -1.334490239 Reorder the terms: -0.05555555555 + x = -1.334490239 Solving -0.05555555555 + x = -1.334490239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.334490239 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.334490239 + 0.05555555555 x = -1.334490239 + 0.05555555555 Combine like terms: -1.334490239 + 0.05555555555 = -1.27893468345 x = -1.27893468345 Simplifying x = -1.27893468345Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.39004579455, -1.27893468345}
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