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Simplifying -0.5x2 + 0.80x + 3 = 0 Reorder the terms: 3 + 0.80x + -0.5x2 = 0 Solving 3 + 0.80x + -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'. -6 + -1.6x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.6x + x2 = 0 + 6 -1.6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.6x + x2 = 6 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 6 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 6 + 0.64 Combine like terms: 6 + 0.64 = 6.64 0.64 + -1.6x + x2 = 6.64 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 6.64 Calculate the square root of the right side: 2.576819745 Break this problem into two subproblems by setting (x + -0.8) equal to 2.576819745 and -2.576819745.Subproblem 1
x + -0.8 = 2.576819745 Simplifying x + -0.8 = 2.576819745 Reorder the terms: -0.8 + x = 2.576819745 Solving -0.8 + x = 2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.576819745 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.576819745 + 0.8 x = 2.576819745 + 0.8 Combine like terms: 2.576819745 + 0.8 = 3.376819745 x = 3.376819745 Simplifying x = 3.376819745Subproblem 2
x + -0.8 = -2.576819745 Simplifying x + -0.8 = -2.576819745 Reorder the terms: -0.8 + x = -2.576819745 Solving -0.8 + x = -2.576819745 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.576819745 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.576819745 + 0.8 x = -2.576819745 + 0.8 Combine like terms: -2.576819745 + 0.8 = -1.776819745 x = -1.776819745 Simplifying x = -1.776819745Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.376819745, -1.776819745}
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