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Simplifying 25x2 + -32x + 4 = 0 Reorder the terms: 4 + -32x + 25x2 = 0 Solving 4 + -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'. 0.16 + -1.28x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -1.28x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -1.28x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -1.28x + x2 = 0 + -0.16 -1.28x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -1.28x + x2 = -0.16 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 = -0.16 + 0.4096 Reorder the terms: 0.4096 + -1.28x + x2 = -0.16 + 0.4096 Combine like terms: -0.16 + 0.4096 = 0.2496 0.4096 + -1.28x + x2 = 0.2496 Factor a perfect square on the left side: (x + -0.64)(x + -0.64) = 0.2496 Calculate the square root of the right side: 0.49959984 Break this problem into two subproblems by setting (x + -0.64) equal to 0.49959984 and -0.49959984.Subproblem 1
x + -0.64 = 0.49959984 Simplifying x + -0.64 = 0.49959984 Reorder the terms: -0.64 + x = 0.49959984 Solving -0.64 + x = 0.49959984 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 = 0.49959984 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = 0.49959984 + 0.64 x = 0.49959984 + 0.64 Combine like terms: 0.49959984 + 0.64 = 1.13959984 x = 1.13959984 Simplifying x = 1.13959984Subproblem 2
x + -0.64 = -0.49959984 Simplifying x + -0.64 = -0.49959984 Reorder the terms: -0.64 + x = -0.49959984 Solving -0.64 + x = -0.49959984 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 = -0.49959984 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + x = -0.49959984 + 0.64 x = -0.49959984 + 0.64 Combine like terms: -0.49959984 + 0.64 = 0.14040016 x = 0.14040016 Simplifying x = 0.14040016Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.13959984, 0.14040016}
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