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Simplifying 0.5x2 + -3x + -9.4 = 0 Reorder the terms: -9.4 + -3x + 0.5x2 = 0 Solving -9.4 + -3x + 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'. -18.8 + -6x + x2 = 0 Move the constant term to the right: Add '18.8' to each side of the equation. -18.8 + -6x + 18.8 + x2 = 0 + 18.8 Reorder the terms: -18.8 + 18.8 + -6x + x2 = 0 + 18.8 Combine like terms: -18.8 + 18.8 = 0.0 0.0 + -6x + x2 = 0 + 18.8 -6x + x2 = 0 + 18.8 Combine like terms: 0 + 18.8 = 18.8 -6x + x2 = 18.8 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 18.8 + 9 Reorder the terms: 9 + -6x + x2 = 18.8 + 9 Combine like terms: 18.8 + 9 = 27.8 9 + -6x + x2 = 27.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 27.8 Calculate the square root of the right side: 5.272570531 Break this problem into two subproblems by setting (x + -3) equal to 5.272570531 and -5.272570531.Subproblem 1
x + -3 = 5.272570531 Simplifying x + -3 = 5.272570531 Reorder the terms: -3 + x = 5.272570531 Solving -3 + x = 5.272570531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.272570531 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.272570531 + 3 x = 5.272570531 + 3 Combine like terms: 5.272570531 + 3 = 8.272570531 x = 8.272570531 Simplifying x = 8.272570531Subproblem 2
x + -3 = -5.272570531 Simplifying x + -3 = -5.272570531 Reorder the terms: -3 + x = -5.272570531 Solving -3 + x = -5.272570531 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.272570531 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.272570531 + 3 x = -5.272570531 + 3 Combine like terms: -5.272570531 + 3 = -2.272570531 x = -2.272570531 Simplifying x = -2.272570531Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.272570531, -2.272570531}
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