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Simplifying 20x2 + -32x + -565 = 0 Reorder the terms: -565 + -32x + 20x2 = 0 Solving -565 + -32x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -28.25 + -1.6x + x2 = 0 Move the constant term to the right: Add '28.25' to each side of the equation. -28.25 + -1.6x + 28.25 + x2 = 0 + 28.25 Reorder the terms: -28.25 + 28.25 + -1.6x + x2 = 0 + 28.25 Combine like terms: -28.25 + 28.25 = 0.00 0.00 + -1.6x + x2 = 0 + 28.25 -1.6x + x2 = 0 + 28.25 Combine like terms: 0 + 28.25 = 28.25 -1.6x + x2 = 28.25 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 = 28.25 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 28.25 + 0.64 Combine like terms: 28.25 + 0.64 = 28.89 0.64 + -1.6x + x2 = 28.89 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 28.89 Calculate the square root of the right side: 5.37494186 Break this problem into two subproblems by setting (x + -0.8) equal to 5.37494186 and -5.37494186.Subproblem 1
x + -0.8 = 5.37494186 Simplifying x + -0.8 = 5.37494186 Reorder the terms: -0.8 + x = 5.37494186 Solving -0.8 + x = 5.37494186 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 = 5.37494186 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 5.37494186 + 0.8 x = 5.37494186 + 0.8 Combine like terms: 5.37494186 + 0.8 = 6.17494186 x = 6.17494186 Simplifying x = 6.17494186Subproblem 2
x + -0.8 = -5.37494186 Simplifying x + -0.8 = -5.37494186 Reorder the terms: -0.8 + x = -5.37494186 Solving -0.8 + x = -5.37494186 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 = -5.37494186 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -5.37494186 + 0.8 x = -5.37494186 + 0.8 Combine like terms: -5.37494186 + 0.8 = -4.57494186 x = -4.57494186 Simplifying x = -4.57494186Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.17494186, -4.57494186}
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