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Simplifying 1.9x2 + -1x + -350 = 5x + -9 Reorder the terms: -350 + -1x + 1.9x2 = 5x + -9 Reorder the terms: -350 + -1x + 1.9x2 = -9 + 5x Solving -350 + -1x + 1.9x2 = -9 + 5x Solving for variable 'x'. Reorder the terms: -350 + 9 + -1x + -5x + 1.9x2 = -9 + 5x + 9 + -5x Combine like terms: -350 + 9 = -341 -341 + -1x + -5x + 1.9x2 = -9 + 5x + 9 + -5x Combine like terms: -1x + -5x = -6x -341 + -6x + 1.9x2 = -9 + 5x + 9 + -5x Reorder the terms: -341 + -6x + 1.9x2 = -9 + 9 + 5x + -5x Combine like terms: -9 + 9 = 0 -341 + -6x + 1.9x2 = 0 + 5x + -5x -341 + -6x + 1.9x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -341 + -6x + 1.9x2 = 0 Begin completing the square. Divide all terms by 1.9 the coefficient of the squared term: Divide each side by '1.9'. -179.4736842 + -3.157894737x + x2 = 0 Move the constant term to the right: Add '179.4736842' to each side of the equation. -179.4736842 + -3.157894737x + 179.4736842 + x2 = 0 + 179.4736842 Reorder the terms: -179.4736842 + 179.4736842 + -3.157894737x + x2 = 0 + 179.4736842 Combine like terms: -179.4736842 + 179.4736842 = 0.0000000 0.0000000 + -3.157894737x + x2 = 0 + 179.4736842 -3.157894737x + x2 = 0 + 179.4736842 Combine like terms: 0 + 179.4736842 = 179.4736842 -3.157894737x + x2 = 179.4736842 The x term is -3.157894737x. Take half its coefficient (-1.578947369). Square it (2.493074794) and add it to both sides. Add '2.493074794' to each side of the equation. -3.157894737x + 2.493074794 + x2 = 179.4736842 + 2.493074794 Reorder the terms: 2.493074794 + -3.157894737x + x2 = 179.4736842 + 2.493074794 Combine like terms: 179.4736842 + 2.493074794 = 181.966758994 2.493074794 + -3.157894737x + x2 = 181.966758994 Factor a perfect square on the left side: (x + -1.578947369)(x + -1.578947369) = 181.966758994 Calculate the square root of the right side: 13.489505513 Break this problem into two subproblems by setting (x + -1.578947369) equal to 13.489505513 and -13.489505513.Subproblem 1
x + -1.578947369 = 13.489505513 Simplifying x + -1.578947369 = 13.489505513 Reorder the terms: -1.578947369 + x = 13.489505513 Solving -1.578947369 + x = 13.489505513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.578947369' to each side of the equation. -1.578947369 + 1.578947369 + x = 13.489505513 + 1.578947369 Combine like terms: -1.578947369 + 1.578947369 = 0.000000000 0.000000000 + x = 13.489505513 + 1.578947369 x = 13.489505513 + 1.578947369 Combine like terms: 13.489505513 + 1.578947369 = 15.068452882 x = 15.068452882 Simplifying x = 15.068452882Subproblem 2
x + -1.578947369 = -13.489505513 Simplifying x + -1.578947369 = -13.489505513 Reorder the terms: -1.578947369 + x = -13.489505513 Solving -1.578947369 + x = -13.489505513 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.578947369' to each side of the equation. -1.578947369 + 1.578947369 + x = -13.489505513 + 1.578947369 Combine like terms: -1.578947369 + 1.578947369 = 0.000000000 0.000000000 + x = -13.489505513 + 1.578947369 x = -13.489505513 + 1.578947369 Combine like terms: -13.489505513 + 1.578947369 = -11.910558144 x = -11.910558144 Simplifying x = -11.910558144Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.068452882, -11.910558144}
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