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Simplifying -16x2 + 17x + 7 = 11 Reorder the terms: 7 + 17x + -16x2 = 11 Solving 7 + 17x + -16x2 = 11 Solving for variable 'x'. Reorder the terms: 7 + -11 + 17x + -16x2 = 11 + -11 Combine like terms: 7 + -11 = -4 -4 + 17x + -16x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -4 + 17x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 0.25 + -1.0625x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.0625x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.0625x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.0625x + x2 = 0 + -0.25 -1.0625x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.0625x + x2 = -0.25 The x term is -1.0625x. Take half its coefficient (-0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. -1.0625x + 0.2822265625 + x2 = -0.25 + 0.2822265625 Reorder the terms: 0.2822265625 + -1.0625x + x2 = -0.25 + 0.2822265625 Combine like terms: -0.25 + 0.2822265625 = 0.0322265625 0.2822265625 + -1.0625x + x2 = 0.0322265625 Factor a perfect square on the left side: (x + -0.53125)(x + -0.53125) = 0.0322265625 Calculate the square root of the right side: 0.179517583 Break this problem into two subproblems by setting (x + -0.53125) equal to 0.179517583 and -0.179517583.Subproblem 1
x + -0.53125 = 0.179517583 Simplifying x + -0.53125 = 0.179517583 Reorder the terms: -0.53125 + x = 0.179517583 Solving -0.53125 + x = 0.179517583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = 0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = 0.179517583 + 0.53125 x = 0.179517583 + 0.53125 Combine like terms: 0.179517583 + 0.53125 = 0.710767583 x = 0.710767583 Simplifying x = 0.710767583Subproblem 2
x + -0.53125 = -0.179517583 Simplifying x + -0.53125 = -0.179517583 Reorder the terms: -0.53125 + x = -0.179517583 Solving -0.53125 + x = -0.179517583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.53125' to each side of the equation. -0.53125 + 0.53125 + x = -0.179517583 + 0.53125 Combine like terms: -0.53125 + 0.53125 = 0.00000 0.00000 + x = -0.179517583 + 0.53125 x = -0.179517583 + 0.53125 Combine like terms: -0.179517583 + 0.53125 = 0.351732417 x = 0.351732417 Simplifying x = 0.351732417Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.710767583, 0.351732417}
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