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Simplifying 0 = 10x2 + -11x + -15 Reorder the terms: 0 = -15 + -11x + 10x2 Solving 0 = -15 + -11x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 15 = 15 15 + 11x + -10x2 = -15 + -11x + 10x2 + 15 + 11x + -10x2 Reorder the terms: 15 + 11x + -10x2 = -15 + 15 + -11x + 11x + 10x2 + -10x2 Combine like terms: -15 + 15 = 0 15 + 11x + -10x2 = 0 + -11x + 11x + 10x2 + -10x2 15 + 11x + -10x2 = -11x + 11x + 10x2 + -10x2 Combine like terms: -11x + 11x = 0 15 + 11x + -10x2 = 0 + 10x2 + -10x2 15 + 11x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 15 + 11x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.5 + -1.1x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1.1x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1.1x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1.1x + x2 = 0 + 1.5 -1.1x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1.1x + x2 = 1.5 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 1.5 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 1.5 + 0.3025 Combine like terms: 1.5 + 0.3025 = 1.8025 0.3025 + -1.1x + x2 = 1.8025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 1.8025 Calculate the square root of the right side: 1.342572158 Break this problem into two subproblems by setting (x + -0.55) equal to 1.342572158 and -1.342572158.Subproblem 1
x + -0.55 = 1.342572158 Simplifying x + -0.55 = 1.342572158 Reorder the terms: -0.55 + x = 1.342572158 Solving -0.55 + x = 1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.342572158 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.342572158 + 0.55 x = 1.342572158 + 0.55 Combine like terms: 1.342572158 + 0.55 = 1.892572158 x = 1.892572158 Simplifying x = 1.892572158Subproblem 2
x + -0.55 = -1.342572158 Simplifying x + -0.55 = -1.342572158 Reorder the terms: -0.55 + x = -1.342572158 Solving -0.55 + x = -1.342572158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.342572158 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.342572158 + 0.55 x = -1.342572158 + 0.55 Combine like terms: -1.342572158 + 0.55 = -0.792572158 x = -0.792572158 Simplifying x = -0.792572158Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892572158, -0.792572158}
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