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Simplifying 5x2 + 32x + 32 = 0 Reorder the terms: 32 + 32x + 5x2 = 0 Solving 32 + 32x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 6.4 + 6.4x + x2 = 0 Move the constant term to the right: Add '-6.4' to each side of the equation. 6.4 + 6.4x + -6.4 + x2 = 0 + -6.4 Reorder the terms: 6.4 + -6.4 + 6.4x + x2 = 0 + -6.4 Combine like terms: 6.4 + -6.4 = 0.0 0.0 + 6.4x + x2 = 0 + -6.4 6.4x + x2 = 0 + -6.4 Combine like terms: 0 + -6.4 = -6.4 6.4x + x2 = -6.4 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = -6.4 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = -6.4 + 10.24 Combine like terms: -6.4 + 10.24 = 3.84 10.24 + 6.4x + x2 = 3.84 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + 3.2) equal to 1.959591794 and -1.959591794.Subproblem 1
x + 3.2 = 1.959591794 Simplifying x + 3.2 = 1.959591794 Reorder the terms: 3.2 + x = 1.959591794 Solving 3.2 + x = 1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 1.959591794 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 1.959591794 + -3.2 x = 1.959591794 + -3.2 Combine like terms: 1.959591794 + -3.2 = -1.240408206 x = -1.240408206 Simplifying x = -1.240408206Subproblem 2
x + 3.2 = -1.959591794 Simplifying x + 3.2 = -1.959591794 Reorder the terms: 3.2 + x = -1.959591794 Solving 3.2 + x = -1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -1.959591794 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -1.959591794 + -3.2 x = -1.959591794 + -3.2 Combine like terms: -1.959591794 + -3.2 = -5.159591794 x = -5.159591794 Simplifying x = -5.159591794Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.240408206, -5.159591794}
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