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Simplifying -5x2 + 32x + 12 = 0 Reorder the terms: 12 + 32x + -5x2 = 0 Solving 12 + 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'. -2.4 + -6.4x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -6.4x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -6.4x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -6.4x + x2 = 0 + 2.4 -6.4x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -6.4x + x2 = 2.4 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 = 2.4 + 10.24 Reorder the terms: 10.24 + -6.4x + x2 = 2.4 + 10.24 Combine like terms: 2.4 + 10.24 = 12.64 10.24 + -6.4x + x2 = 12.64 Factor a perfect square on the left side: (x + -3.2)(x + -3.2) = 12.64 Calculate the square root of the right side: 3.555277767 Break this problem into two subproblems by setting (x + -3.2) equal to 3.555277767 and -3.555277767.Subproblem 1
x + -3.2 = 3.555277767 Simplifying x + -3.2 = 3.555277767 Reorder the terms: -3.2 + x = 3.555277767 Solving -3.2 + x = 3.555277767 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 = 3.555277767 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = 3.555277767 + 3.2 x = 3.555277767 + 3.2 Combine like terms: 3.555277767 + 3.2 = 6.755277767 x = 6.755277767 Simplifying x = 6.755277767Subproblem 2
x + -3.2 = -3.555277767 Simplifying x + -3.2 = -3.555277767 Reorder the terms: -3.2 + x = -3.555277767 Solving -3.2 + x = -3.555277767 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 = -3.555277767 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + x = -3.555277767 + 3.2 x = -3.555277767 + 3.2 Combine like terms: -3.555277767 + 3.2 = -0.355277767 x = -0.355277767 Simplifying x = -0.355277767Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.755277767, -0.355277767}
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