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Simplifying 3.2 = 8x + -5x2 Solving 3.2 = 8x + -5x2 Solving for variable 'x'. Reorder the terms: 3.2 + -8x + 5x2 = 8x + -8x + -5x2 + 5x2 Combine like terms: 8x + -8x = 0 3.2 + -8x + 5x2 = 0 + -5x2 + 5x2 3.2 + -8x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 3.2 + -8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.64 + -1.6x + x2 = 0 Move the constant term to the right: Add '-0.64' to each side of the equation. 0.64 + -1.6x + -0.64 + x2 = 0 + -0.64 Reorder the terms: 0.64 + -0.64 + -1.6x + x2 = 0 + -0.64 Combine like terms: 0.64 + -0.64 = 0.00 0.00 + -1.6x + x2 = 0 + -0.64 -1.6x + x2 = 0 + -0.64 Combine like terms: 0 + -0.64 = -0.64 -1.6x + x2 = -0.64 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -0.64 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -0.64 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.64 + -1.6x + x2 = 0.00 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -0.8) equal to 0.00 and 0.00.Subproblem 1
x + -0.8 = 0.00 Simplifying x + -0.8 = 0.00 Reorder the terms: -0.8 + x = 0.00 Solving -0.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.00 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.00 + 0.8 x = 0.00 + 0.8 Combine like terms: 0.00 + 0.8 = 0.8 x = 0.8 Simplifying x = 0.8Subproblem 2
x + -0.8 = 0.00 Simplifying x + -0.8 = 0.00 Reorder the terms: -0.8 + x = 0.00 Solving -0.8 + x = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 0.00 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 0.00 + 0.8 x = 0.00 + 0.8 Combine like terms: 0.00 + 0.8 = 0.8 x = 0.8 Simplifying x = 0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8, 0.8}
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