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Simplifying 25x2 + -32x + 6 = 0 Reorder the terms: 6 + -32x + 25x2 = 0 Solving 6 + -32x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.24 + -1.28x + x2 = 0 Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + -1.28x + -0.24 + x2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + -1.28x + x2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + -1.28x + x2 = 0 + -0.24 -1.28x + x2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 -1.28x + x2 = -0.24 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 = -0.24 + 0.4096 Reorder the terms: 0.4096 + -1.28x + x2 = -0.24 + 0.4096 Combine like terms: -0.24 + 0.4096 = 0.1696 0.4096 + -1.28x + x2 = 0.1696 Factor a perfect square on the left side: (x + -0.64)(x + -0.64) = 0.1696 Calculate the square root of the right side: 0.411825206 Break this problem into two subproblems by setting (x + -0.64) equal to 0.411825206 and -0.411825206.Subproblem 1
x + -0.64 = 0.411825206 Simplifying x + -0.64 = 0.411825206 Reorder the terms: -0.64 + x = 0.411825206 Solving -0.64 + x = 0.411825206 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 = 0.411825206 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = 0.411825206 + 0.64 x = 0.411825206 + 0.64 Combine like terms: 0.411825206 + 0.64 = 1.051825206 x = 1.051825206 Simplifying x = 1.051825206Subproblem 2
x + -0.64 = -0.411825206 Simplifying x + -0.64 = -0.411825206 Reorder the terms: -0.64 + x = -0.411825206 Solving -0.64 + x = -0.411825206 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 = -0.411825206 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = -0.411825206 + 0.64 x = -0.411825206 + 0.64 Combine like terms: -0.411825206 + 0.64 = 0.228174794 x = 0.228174794 Simplifying x = 0.228174794Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.051825206, 0.228174794}
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