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Simplifying -16x2 + 55x = 26 Reorder the terms: 55x + -16x2 = 26 Solving 55x + -16x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + 55x + -16x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 55x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 1.625 + -3.4375x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -3.4375x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -3.4375x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -3.4375x + x2 = 0 + -1.625 -3.4375x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -3.4375x + x2 = -1.625 The x term is -3.4375x. Take half its coefficient (-1.71875). Square it (2.954101563) and add it to both sides. Add '2.954101563' to each side of the equation. -3.4375x + 2.954101563 + x2 = -1.625 + 2.954101563 Reorder the terms: 2.954101563 + -3.4375x + x2 = -1.625 + 2.954101563 Combine like terms: -1.625 + 2.954101563 = 1.329101563 2.954101563 + -3.4375x + x2 = 1.329101563 Factor a perfect square on the left side: (x + -1.71875)(x + -1.71875) = 1.329101563 Calculate the square root of the right side: 1.152866672 Break this problem into two subproblems by setting (x + -1.71875) equal to 1.152866672 and -1.152866672.Subproblem 1
x + -1.71875 = 1.152866672 Simplifying x + -1.71875 = 1.152866672 Reorder the terms: -1.71875 + x = 1.152866672 Solving -1.71875 + x = 1.152866672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = 1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = 1.152866672 + 1.71875 x = 1.152866672 + 1.71875 Combine like terms: 1.152866672 + 1.71875 = 2.871616672 x = 2.871616672 Simplifying x = 2.871616672Subproblem 2
x + -1.71875 = -1.152866672 Simplifying x + -1.71875 = -1.152866672 Reorder the terms: -1.71875 + x = -1.152866672 Solving -1.71875 + x = -1.152866672 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + x = -1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + x = -1.152866672 + 1.71875 x = -1.152866672 + 1.71875 Combine like terms: -1.152866672 + 1.71875 = 0.565883328 x = 0.565883328 Simplifying x = 0.565883328Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.871616672, 0.565883328}
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