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Simplifying 0.5x2 + -0.45x + -0.3 = 0 Reorder the terms: -0.3 + -0.45x + 0.5x2 = 0 Solving -0.3 + -0.45x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -0.6 + -0.9x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.9x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.9x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.9x + x2 = 0 + 0.6 -0.9x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.9x + x2 = 0.6 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 = 0.6 + 0.2025 Reorder the terms: 0.2025 + -0.9x + x2 = 0.6 + 0.2025 Combine like terms: 0.6 + 0.2025 = 0.8025 0.2025 + -0.9x + x2 = 0.8025 Factor a perfect square on the left side: (x + -0.45)(x + -0.45) = 0.8025 Calculate the square root of the right side: 0.895823643 Break this problem into two subproblems by setting (x + -0.45) equal to 0.895823643 and -0.895823643.Subproblem 1
x + -0.45 = 0.895823643 Simplifying x + -0.45 = 0.895823643 Reorder the terms: -0.45 + x = 0.895823643 Solving -0.45 + x = 0.895823643 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 = 0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = 0.895823643 + 0.45 x = 0.895823643 + 0.45 Combine like terms: 0.895823643 + 0.45 = 1.345823643 x = 1.345823643 Simplifying x = 1.345823643Subproblem 2
x + -0.45 = -0.895823643 Simplifying x + -0.45 = -0.895823643 Reorder the terms: -0.45 + x = -0.895823643 Solving -0.45 + x = -0.895823643 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 = -0.895823643 + 0.45 Combine like terms: -0.45 + 0.45 = 0.00 0.00 + x = -0.895823643 + 0.45 x = -0.895823643 + 0.45 Combine like terms: -0.895823643 + 0.45 = -0.445823643 x = -0.445823643 Simplifying x = -0.445823643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.345823643, -0.445823643}
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