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Simplifying -10x2 + -9x + 24 = 0 Reorder the terms: 24 + -9x + -10x2 = 0 Solving 24 + -9x + -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'. -2.4 + 0.9x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.9x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.9x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.9x + x2 = 0 + 2.4 0.9x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.9x + x2 = 2.4 The x term is 0.9x. Take half its coefficient (0.45). Square it (0.2025) and add it to both sides. Add '0.2025' to each side of the equation. 0.9x + 0.2025 + x2 = 2.4 + 0.2025 Reorder the terms: 0.2025 + 0.9x + x2 = 2.4 + 0.2025 Combine like terms: 2.4 + 0.2025 = 2.6025 0.2025 + 0.9x + x2 = 2.6025 Factor a perfect square on the left side: (x + 0.45)(x + 0.45) = 2.6025 Calculate the square root of the right side: 1.61322658 Break this problem into two subproblems by setting (x + 0.45) equal to 1.61322658 and -1.61322658.Subproblem 1
x + 0.45 = 1.61322658 Simplifying x + 0.45 = 1.61322658 Reorder the terms: 0.45 + x = 1.61322658 Solving 0.45 + x = 1.61322658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = 1.61322658 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = 1.61322658 + -0.45 x = 1.61322658 + -0.45 Combine like terms: 1.61322658 + -0.45 = 1.16322658 x = 1.16322658 Simplifying x = 1.16322658Subproblem 2
x + 0.45 = -1.61322658 Simplifying x + 0.45 = -1.61322658 Reorder the terms: 0.45 + x = -1.61322658 Solving 0.45 + x = -1.61322658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.45' to each side of the equation. 0.45 + -0.45 + x = -1.61322658 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + x = -1.61322658 + -0.45 x = -1.61322658 + -0.45 Combine like terms: -1.61322658 + -0.45 = -2.06322658 x = -2.06322658 Simplifying x = -2.06322658Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16322658, -2.06322658}
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