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Simplifying 2x2 + -3x + 0.91 = 0 Reorder the terms: 0.91 + -3x + 2x2 = 0 Solving 0.91 + -3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.455 + -1.5x + x2 = 0 Move the constant term to the right: Add '-0.455' to each side of the equation. 0.455 + -1.5x + -0.455 + x2 = 0 + -0.455 Reorder the terms: 0.455 + -0.455 + -1.5x + x2 = 0 + -0.455 Combine like terms: 0.455 + -0.455 = 0.000 0.000 + -1.5x + x2 = 0 + -0.455 -1.5x + x2 = 0 + -0.455 Combine like terms: 0 + -0.455 = -0.455 -1.5x + x2 = -0.455 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 = -0.455 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -0.455 + 0.5625 Combine like terms: -0.455 + 0.5625 = 0.1075 0.5625 + -1.5x + x2 = 0.1075 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 0.1075 Calculate the square root of the right side: 0.327871926 Break this problem into two subproblems by setting (x + -0.75) equal to 0.327871926 and -0.327871926.Subproblem 1
x + -0.75 = 0.327871926 Simplifying x + -0.75 = 0.327871926 Reorder the terms: -0.75 + x = 0.327871926 Solving -0.75 + x = 0.327871926 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 = 0.327871926 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 0.327871926 + 0.75 x = 0.327871926 + 0.75 Combine like terms: 0.327871926 + 0.75 = 1.077871926 x = 1.077871926 Simplifying x = 1.077871926Subproblem 2
x + -0.75 = -0.327871926 Simplifying x + -0.75 = -0.327871926 Reorder the terms: -0.75 + x = -0.327871926 Solving -0.75 + x = -0.327871926 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 = -0.327871926 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -0.327871926 + 0.75 x = -0.327871926 + 0.75 Combine like terms: -0.327871926 + 0.75 = 0.422128074 x = 0.422128074 Simplifying x = 0.422128074Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.077871926, 0.422128074}
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