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Simplifying 3x + -2x2 = 0.28 Solving 3x + -2x2 = 0.28 Solving for variable 'x'. Reorder the terms: -0.28 + 3x + -2x2 = 0.28 + -0.28 Combine like terms: 0.28 + -0.28 = 0.00 -0.28 + 3x + -2x2 = 0.00 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.14 + -1.5x + x2 = 0.00 Move the constant term to the right: Add '-0.14' to each side of the equation. 0.14 + -1.5x + -0.14 + x2 = 0.00 + -0.14 Reorder the terms: 0.14 + -0.14 + -1.5x + x2 = 0.00 + -0.14 Combine like terms: 0.14 + -0.14 = 0.00 0.00 + -1.5x + x2 = 0.00 + -0.14 -1.5x + x2 = 0.00 + -0.14 Combine like terms: 0.00 + -0.14 = -0.14 -1.5x + x2 = -0.14 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 = -0.14 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.14 + 0.5625 Combine like terms: -0.14 + 0.5625 = 0.4225 0.5625 + -1.5x + x2 = 0.4225 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.4225 Calculate the square root of the right side: 0.65 Break this problem into two subproblems by setting (x + -0.75) equal to 0.65 and -0.65.Subproblem 1
x + -0.75 = 0.65 Simplifying x + -0.75 = 0.65 Reorder the terms: -0.75 + x = 0.65 Solving -0.75 + x = 0.65 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 = 0.65 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.65 + 0.75 x = 0.65 + 0.75 Combine like terms: 0.65 + 0.75 = 1.4 x = 1.4 Simplifying x = 1.4Subproblem 2
x + -0.75 = -0.65 Simplifying x + -0.75 = -0.65 Reorder the terms: -0.75 + x = -0.65 Solving -0.75 + x = -0.65 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 = -0.65 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.65 + 0.75 x = -0.65 + 0.75 Combine like terms: -0.65 + 0.75 = 0.1 x = 0.1 Simplifying x = 0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4, 0.1}
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