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Simplifying -0.2x2 + 0.3x + 2 = 0 Reorder the terms: 2 + 0.3x + -0.2x2 = 0 Solving 2 + 0.3x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. -10 + -1.5x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.5x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -1.5x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.5x + x2 = 0 + 10 -1.5x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.5x + x2 = 10 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 10 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 10 + 0.5625 Combine like terms: 10 + 0.5625 = 10.5625 0.5625 + -1.5x + x2 = 10.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (x + -0.75) equal to 3.25 and -3.25.Subproblem 1
x + -0.75 = 3.25 Simplifying x + -0.75 = 3.25 Reorder the terms: -0.75 + x = 3.25 Solving -0.75 + x = 3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.25 + 0.75 x = 3.25 + 0.75 Combine like terms: 3.25 + 0.75 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -0.75 = -3.25 Simplifying x + -0.75 = -3.25 Reorder the terms: -0.75 + x = -3.25 Solving -0.75 + x = -3.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.25 + 0.75 x = -3.25 + 0.75 Combine like terms: -3.25 + 0.75 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -2.5}
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