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Simplifying 16x2 + 101x = -135 Reorder the terms: 101x + 16x2 = -135 Solving 101x + 16x2 = -135 Solving for variable 'x'. Reorder the terms: 135 + 101x + 16x2 = -135 + 135 Combine like terms: -135 + 135 = 0 135 + 101x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 8.4375 + 6.3125x + x2 = 0 Move the constant term to the right: Add '-8.4375' to each side of the equation. 8.4375 + 6.3125x + -8.4375 + x2 = 0 + -8.4375 Reorder the terms: 8.4375 + -8.4375 + 6.3125x + x2 = 0 + -8.4375 Combine like terms: 8.4375 + -8.4375 = 0.0000 0.0000 + 6.3125x + x2 = 0 + -8.4375 6.3125x + x2 = 0 + -8.4375 Combine like terms: 0 + -8.4375 = -8.4375 6.3125x + x2 = -8.4375 The x term is 6.3125x. Take half its coefficient (3.15625). Square it (9.961914063) and add it to both sides. Add '9.961914063' to each side of the equation. 6.3125x + 9.961914063 + x2 = -8.4375 + 9.961914063 Reorder the terms: 9.961914063 + 6.3125x + x2 = -8.4375 + 9.961914063 Combine like terms: -8.4375 + 9.961914063 = 1.524414063 9.961914063 + 6.3125x + x2 = 1.524414063 Factor a perfect square on the left side: (x + 3.15625)(x + 3.15625) = 1.524414063 Calculate the square root of the right side: 1.234671642 Break this problem into two subproblems by setting (x + 3.15625) equal to 1.234671642 and -1.234671642.Subproblem 1
x + 3.15625 = 1.234671642 Simplifying x + 3.15625 = 1.234671642 Reorder the terms: 3.15625 + x = 1.234671642 Solving 3.15625 + x = 1.234671642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.15625' to each side of the equation. 3.15625 + -3.15625 + x = 1.234671642 + -3.15625 Combine like terms: 3.15625 + -3.15625 = 0.00000 0.00000 + x = 1.234671642 + -3.15625 x = 1.234671642 + -3.15625 Combine like terms: 1.234671642 + -3.15625 = -1.921578358 x = -1.921578358 Simplifying x = -1.921578358Subproblem 2
x + 3.15625 = -1.234671642 Simplifying x + 3.15625 = -1.234671642 Reorder the terms: 3.15625 + x = -1.234671642 Solving 3.15625 + x = -1.234671642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.15625' to each side of the equation. 3.15625 + -3.15625 + x = -1.234671642 + -3.15625 Combine like terms: 3.15625 + -3.15625 = 0.00000 0.00000 + x = -1.234671642 + -3.15625 x = -1.234671642 + -3.15625 Combine like terms: -1.234671642 + -3.15625 = -4.390921642 x = -4.390921642 Simplifying x = -4.390921642Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.921578358, -4.390921642}
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