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Simplifying 5x2 + -3x + -32 = 0 Reorder the terms: -32 + -3x + 5x2 = 0 Solving -32 + -3x + 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 + -0.6x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + -0.6x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + -0.6x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + -0.6x + x2 = 0 + 6.4 -0.6x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 -0.6x + x2 = 6.4 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 6.4 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 6.4 + 0.09 Combine like terms: 6.4 + 0.09 = 6.49 0.09 + -0.6x + x2 = 6.49 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (x + -0.3) equal to 2.547547841 and -2.547547841.Subproblem 1
x + -0.3 = 2.547547841 Simplifying x + -0.3 = 2.547547841 Reorder the terms: -0.3 + x = 2.547547841 Solving -0.3 + x = 2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.547547841 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.547547841 + 0.3 x = 2.547547841 + 0.3 Combine like terms: 2.547547841 + 0.3 = 2.847547841 x = 2.847547841 Simplifying x = 2.847547841Subproblem 2
x + -0.3 = -2.547547841 Simplifying x + -0.3 = -2.547547841 Reorder the terms: -0.3 + x = -2.547547841 Solving -0.3 + x = -2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.547547841 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.547547841 + 0.3 x = -2.547547841 + 0.3 Combine like terms: -2.547547841 + 0.3 = -2.247547841 x = -2.247547841 Simplifying x = -2.247547841Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.847547841, -2.247547841}
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