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Simplifying x2 + 19x + 18 = 10x2 + 14x + -19 Reorder the terms: 18 + 19x + x2 = 10x2 + 14x + -19 Reorder the terms: 18 + 19x + x2 = -19 + 14x + 10x2 Solving 18 + 19x + x2 = -19 + 14x + 10x2 Solving for variable 'x'. Reorder the terms: 18 + 19 + 19x + -14x + x2 + -10x2 = -19 + 14x + 10x2 + 19 + -14x + -10x2 Combine like terms: 18 + 19 = 37 37 + 19x + -14x + x2 + -10x2 = -19 + 14x + 10x2 + 19 + -14x + -10x2 Combine like terms: 19x + -14x = 5x 37 + 5x + x2 + -10x2 = -19 + 14x + 10x2 + 19 + -14x + -10x2 Combine like terms: x2 + -10x2 = -9x2 37 + 5x + -9x2 = -19 + 14x + 10x2 + 19 + -14x + -10x2 Reorder the terms: 37 + 5x + -9x2 = -19 + 19 + 14x + -14x + 10x2 + -10x2 Combine like terms: -19 + 19 = 0 37 + 5x + -9x2 = 0 + 14x + -14x + 10x2 + -10x2 37 + 5x + -9x2 = 14x + -14x + 10x2 + -10x2 Combine like terms: 14x + -14x = 0 37 + 5x + -9x2 = 0 + 10x2 + -10x2 37 + 5x + -9x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 37 + 5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -4.111111111 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '4.111111111' to each side of the equation. -4.111111111 + -0.5555555556x + 4.111111111 + x2 = 0 + 4.111111111 Reorder the terms: -4.111111111 + 4.111111111 + -0.5555555556x + x2 = 0 + 4.111111111 Combine like terms: -4.111111111 + 4.111111111 = 0.000000000 0.000000000 + -0.5555555556x + x2 = 0 + 4.111111111 -0.5555555556x + x2 = 0 + 4.111111111 Combine like terms: 0 + 4.111111111 = 4.111111111 -0.5555555556x + x2 = 4.111111111 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 = 4.111111111 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 4.111111111 + 0.07716049384 Combine like terms: 4.111111111 + 0.07716049384 = 4.18827160484 0.07716049384 + -0.5555555556x + x2 = 4.18827160484 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 4.18827160484 Calculate the square root of the right side: 2.046526717 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 2.046526717 and -2.046526717.Subproblem 1
x + -0.2777777778 = 2.046526717 Simplifying x + -0.2777777778 = 2.046526717 Reorder the terms: -0.2777777778 + x = 2.046526717 Solving -0.2777777778 + x = 2.046526717 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 = 2.046526717 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 2.046526717 + 0.2777777778 x = 2.046526717 + 0.2777777778 Combine like terms: 2.046526717 + 0.2777777778 = 2.3243044948 x = 2.3243044948 Simplifying x = 2.3243044948Subproblem 2
x + -0.2777777778 = -2.046526717 Simplifying x + -0.2777777778 = -2.046526717 Reorder the terms: -0.2777777778 + x = -2.046526717 Solving -0.2777777778 + x = -2.046526717 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 = -2.046526717 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -2.046526717 + 0.2777777778 x = -2.046526717 + 0.2777777778 Combine like terms: -2.046526717 + 0.2777777778 = -1.7687489392 x = -1.7687489392 Simplifying x = -1.7687489392Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3243044948, -1.7687489392}
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