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Simplifying -16x2 + 27.2x = -9.6 Reorder the terms: 27.2x + -16x2 = -9.6 Solving 27.2x + -16x2 = -9.6 Solving for variable 'x'. Reorder the terms: 9.6 + 27.2x + -16x2 = -9.6 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 9.6 + 27.2x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.6 + -1.7x + x2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -1.7x + 0.6 + x2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -1.7x + x2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -1.7x + x2 = 0.0 + 0.6 -1.7x + x2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -1.7x + x2 = 0.6 The x term is -1.7x. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7x + 0.7225 + x2 = 0.6 + 0.7225 Reorder the terms: 0.7225 + -1.7x + x2 = 0.6 + 0.7225 Combine like terms: 0.6 + 0.7225 = 1.3225 0.7225 + -1.7x + x2 = 1.3225 Factor a perfect square on the left side: (x + -0.85)(x + -0.85) = 1.3225 Calculate the square root of the right side: 1.15 Break this problem into two subproblems by setting (x + -0.85) equal to 1.15 and -1.15.Subproblem 1
x + -0.85 = 1.15 Simplifying x + -0.85 = 1.15 Reorder the terms: -0.85 + x = 1.15 Solving -0.85 + x = 1.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = 1.15 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = 1.15 + 0.85 x = 1.15 + 0.85 Combine like terms: 1.15 + 0.85 = 2 x = 2 Simplifying x = 2Subproblem 2
x + -0.85 = -1.15 Simplifying x + -0.85 = -1.15 Reorder the terms: -0.85 + x = -1.15 Solving -0.85 + x = -1.15 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + x = -1.15 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + x = -1.15 + 0.85 x = -1.15 + 0.85 Combine like terms: -1.15 + 0.85 = -0.3 x = -0.3 Simplifying x = -0.3Solution
The solution to the problem is based on the solutions from the subproblems. x = {2, -0.3}
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