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Simplifying 10x2 + -11x + -9 = 0 Reorder the terms: -9 + -11x + 10x2 = 0 Solving -9 + -11x + 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 + -1.1x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + -1.1x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + -1.1x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + -1.1x + x2 = 0 + 0.9 -1.1x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 -1.1x + x2 = 0.9 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 = 0.9 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 0.9 + 0.3025 Combine like terms: 0.9 + 0.3025 = 1.2025 0.3025 + -1.1x + x2 = 1.2025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 1.2025 Calculate the square root of the right side: 1.09658561 Break this problem into two subproblems by setting (x + -0.55) equal to 1.09658561 and -1.09658561.Subproblem 1
x + -0.55 = 1.09658561 Simplifying x + -0.55 = 1.09658561 Reorder the terms: -0.55 + x = 1.09658561 Solving -0.55 + x = 1.09658561 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 = 1.09658561 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.09658561 + 0.55 x = 1.09658561 + 0.55 Combine like terms: 1.09658561 + 0.55 = 1.64658561 x = 1.64658561 Simplifying x = 1.64658561Subproblem 2
x + -0.55 = -1.09658561 Simplifying x + -0.55 = -1.09658561 Reorder the terms: -0.55 + x = -1.09658561 Solving -0.55 + x = -1.09658561 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 = -1.09658561 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.09658561 + 0.55 x = -1.09658561 + 0.55 Combine like terms: -1.09658561 + 0.55 = -0.54658561 x = -0.54658561 Simplifying x = -0.54658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.64658561, -0.54658561}
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