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Simplifying 16x2 + 29x + -7 = 0 Reorder the terms: -7 + 29x + 16x2 = 0 Solving -7 + 29x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.4375 + 1.8125x + x2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + 1.8125x + 0.4375 + x2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + 1.8125x + x2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + 1.8125x + x2 = 0 + 0.4375 1.8125x + x2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 1.8125x + x2 = 0.4375 The x term is 1.8125x. Take half its coefficient (0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. 1.8125x + 0.8212890625 + x2 = 0.4375 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125x + x2 = 0.4375 + 0.8212890625 Combine like terms: 0.4375 + 0.8212890625 = 1.2587890625 0.8212890625 + 1.8125x + x2 = 1.2587890625 Factor a perfect square on the left side: (x + 0.90625)(x + 0.90625) = 1.2587890625 Calculate the square root of the right side: 1.121957692 Break this problem into two subproblems by setting (x + 0.90625) equal to 1.121957692 and -1.121957692.Subproblem 1
x + 0.90625 = 1.121957692 Simplifying x + 0.90625 = 1.121957692 Reorder the terms: 0.90625 + x = 1.121957692 Solving 0.90625 + x = 1.121957692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = 1.121957692 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = 1.121957692 + -0.90625 x = 1.121957692 + -0.90625 Combine like terms: 1.121957692 + -0.90625 = 0.215707692 x = 0.215707692 Simplifying x = 0.215707692Subproblem 2
x + 0.90625 = -1.121957692 Simplifying x + 0.90625 = -1.121957692 Reorder the terms: 0.90625 + x = -1.121957692 Solving 0.90625 + x = -1.121957692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = -1.121957692 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = -1.121957692 + -0.90625 x = -1.121957692 + -0.90625 Combine like terms: -1.121957692 + -0.90625 = -2.028207692 x = -2.028207692 Simplifying x = -2.028207692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.215707692, -2.028207692}
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