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Simplifying 10x2 + 19x + -9 = 0 Reorder the terms: -9 + 19x + 10x2 = 0 Solving -9 + 19x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 1.9x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 1.9x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 1.9x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 1.9x + x2 = 0 + 0.9 1.9x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 1.9x + x2 = 0.9 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = 0.9 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = 0.9 + 0.9025 Combine like terms: 0.9 + 0.9025 = 1.8025 0.9025 + 1.9x + x2 = 1.8025 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 1.8025 Calculate the square root of the right side: 1.342572158 Break this problem into two subproblems by setting (x + 0.95) equal to 1.342572158 and -1.342572158.Subproblem 1
x + 0.95 = 1.342572158 Simplifying x + 0.95 = 1.342572158 Reorder the terms: 0.95 + x = 1.342572158 Solving 0.95 + x = 1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 1.342572158 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 1.342572158 + -0.95 x = 1.342572158 + -0.95 Combine like terms: 1.342572158 + -0.95 = 0.392572158 x = 0.392572158 Simplifying x = 0.392572158Subproblem 2
x + 0.95 = -1.342572158 Simplifying x + 0.95 = -1.342572158 Reorder the terms: 0.95 + x = -1.342572158 Solving 0.95 + x = -1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -1.342572158 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -1.342572158 + -0.95 x = -1.342572158 + -0.95 Combine like terms: -1.342572158 + -0.95 = -2.292572158 x = -2.292572158 Simplifying x = -2.292572158Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.392572158, -2.292572158}
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