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Simplifying 5x2 + 32x + -93 = 0 Reorder the terms: -93 + 32x + 5x2 = 0 Solving -93 + 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'. -18.6 + 6.4x + x2 = 0 Move the constant term to the right: Add '18.6' to each side of the equation. -18.6 + 6.4x + 18.6 + x2 = 0 + 18.6 Reorder the terms: -18.6 + 18.6 + 6.4x + x2 = 0 + 18.6 Combine like terms: -18.6 + 18.6 = 0.0 0.0 + 6.4x + x2 = 0 + 18.6 6.4x + x2 = 0 + 18.6 Combine like terms: 0 + 18.6 = 18.6 6.4x + x2 = 18.6 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 = 18.6 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = 18.6 + 10.24 Combine like terms: 18.6 + 10.24 = 28.84 10.24 + 6.4x + x2 = 28.84 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 28.84 Calculate the square root of the right side: 5.370288633 Break this problem into two subproblems by setting (x + 3.2) equal to 5.370288633 and -5.370288633.Subproblem 1
x + 3.2 = 5.370288633 Simplifying x + 3.2 = 5.370288633 Reorder the terms: 3.2 + x = 5.370288633 Solving 3.2 + x = 5.370288633 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 = 5.370288633 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 5.370288633 + -3.2 x = 5.370288633 + -3.2 Combine like terms: 5.370288633 + -3.2 = 2.170288633 x = 2.170288633 Simplifying x = 2.170288633Subproblem 2
x + 3.2 = -5.370288633 Simplifying x + 3.2 = -5.370288633 Reorder the terms: 3.2 + x = -5.370288633 Solving 3.2 + x = -5.370288633 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 = -5.370288633 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -5.370288633 + -3.2 x = -5.370288633 + -3.2 Combine like terms: -5.370288633 + -3.2 = -8.570288633 x = -8.570288633 Simplifying x = -8.570288633Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.170288633, -8.570288633}
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