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Simplifying 9x2 + -8x + 2 = 110 Reorder the terms: 2 + -8x + 9x2 = 110 Solving 2 + -8x + 9x2 = 110 Solving for variable 'x'. Reorder the terms: 2 + -110 + -8x + 9x2 = 110 + -110 Combine like terms: 2 + -110 = -108 -108 + -8x + 9x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -108 + -8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -12 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -0.8888888889x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + -0.8888888889x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -0.8888888889x + x2 = 0 + 12 -0.8888888889x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 -0.8888888889x + x2 = 12 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 12 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 12 + 0.1975308642 Combine like terms: 12 + 0.1975308642 = 12.1975308642 0.1975308642 + -0.8888888889x + x2 = 12.1975308642 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 12.1975308642 Calculate the square root of the right side: 3.492496366 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 3.492496366 and -3.492496366.Subproblem 1
x + -0.4444444445 = 3.492496366 Simplifying x + -0.4444444445 = 3.492496366 Reorder the terms: -0.4444444445 + x = 3.492496366 Solving -0.4444444445 + x = 3.492496366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 3.492496366 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 3.492496366 + 0.4444444445 x = 3.492496366 + 0.4444444445 Combine like terms: 3.492496366 + 0.4444444445 = 3.9369408105 x = 3.9369408105 Simplifying x = 3.9369408105Subproblem 2
x + -0.4444444445 = -3.492496366 Simplifying x + -0.4444444445 = -3.492496366 Reorder the terms: -0.4444444445 + x = -3.492496366 Solving -0.4444444445 + x = -3.492496366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -3.492496366 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -3.492496366 + 0.4444444445 x = -3.492496366 + 0.4444444445 Combine like terms: -3.492496366 + 0.4444444445 = -3.0480519215 x = -3.0480519215 Simplifying x = -3.0480519215Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.9369408105, -3.0480519215}
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