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Simplifying 10x2 + 11x + -16 = 16x Reorder the terms: -16 + 11x + 10x2 = 16x Solving -16 + 11x + 10x2 = 16x Solving for variable 'x'. Reorder the terms: -16 + 11x + -16x + 10x2 = 16x + -16x Combine like terms: 11x + -16x = -5x -16 + -5x + 10x2 = 16x + -16x Combine like terms: 16x + -16x = 0 -16 + -5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.6 + -0.5x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.5x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.5x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.5x + x2 = 0 + 1.6 -0.5x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -0.5x + x2 = 1.6 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1.6 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1.6 + 0.0625 Combine like terms: 1.6 + 0.0625 = 1.6625 0.0625 + -0.5x + x2 = 1.6625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 1.6625 Calculate the square root of the right side: 1.289379696 Break this problem into two subproblems by setting (x + -0.25) equal to 1.289379696 and -1.289379696.Subproblem 1
x + -0.25 = 1.289379696 Simplifying x + -0.25 = 1.289379696 Reorder the terms: -0.25 + x = 1.289379696 Solving -0.25 + x = 1.289379696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.289379696 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.289379696 + 0.25 x = 1.289379696 + 0.25 Combine like terms: 1.289379696 + 0.25 = 1.539379696 x = 1.539379696 Simplifying x = 1.539379696Subproblem 2
x + -0.25 = -1.289379696 Simplifying x + -0.25 = -1.289379696 Reorder the terms: -0.25 + x = -1.289379696 Solving -0.25 + x = -1.289379696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.289379696 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.289379696 + 0.25 x = -1.289379696 + 0.25 Combine like terms: -1.289379696 + 0.25 = -1.039379696 x = -1.039379696 Simplifying x = -1.039379696Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.539379696, -1.039379696}
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