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Simplifying 2.5x2 + -3.2x + 1 = 0 Reorder the terms: 1 + -3.2x + 2.5x2 = 0 Solving 1 + -3.2x + 2.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.5 the coefficient of the squared term: Divide each side by '2.5'. 0.4 + -1.28x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.28x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.28x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.28x + x2 = 0 + -0.4 -1.28x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.28x + x2 = -0.4 The x term is -1.28x. Take half its coefficient (-0.64). Square it (0.4096) and add it to both sides. Add '0.4096' to each side of the equation. -1.28x + 0.4096 + x2 = -0.4 + 0.4096 Reorder the terms: 0.4096 + -1.28x + x2 = -0.4 + 0.4096 Combine like terms: -0.4 + 0.4096 = 0.0096 0.4096 + -1.28x + x2 = 0.0096 Factor a perfect square on the left side: (x + -0.64)(x + -0.64) = 0.0096 Calculate the square root of the right side: 0.09797959 Break this problem into two subproblems by setting (x + -0.64) equal to 0.09797959 and -0.09797959.Subproblem 1
x + -0.64 = 0.09797959 Simplifying x + -0.64 = 0.09797959 Reorder the terms: -0.64 + x = 0.09797959 Solving -0.64 + x = 0.09797959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.64' to each side of the equation. -0.64 + 0.64 + x = 0.09797959 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = 0.09797959 + 0.64 x = 0.09797959 + 0.64 Combine like terms: 0.09797959 + 0.64 = 0.73797959 x = 0.73797959 Simplifying x = 0.73797959Subproblem 2
x + -0.64 = -0.09797959 Simplifying x + -0.64 = -0.09797959 Reorder the terms: -0.64 + x = -0.09797959 Solving -0.64 + x = -0.09797959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.64' to each side of the equation. -0.64 + 0.64 + x = -0.09797959 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = -0.09797959 + 0.64 x = -0.09797959 + 0.64 Combine like terms: -0.09797959 + 0.64 = 0.54202041 x = 0.54202041 Simplifying x = 0.54202041Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.73797959, 0.54202041}
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