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Simplifying x = -16x2 + 30x + 8 Reorder the terms: x = 8 + 30x + -16x2 Solving x = 8 + 30x + -16x2 Solving for variable 'x'. Reorder the terms: -8 + x + -30x + 16x2 = 8 + 30x + -16x2 + -8 + -30x + 16x2 Combine like terms: x + -30x = -29x -8 + -29x + 16x2 = 8 + 30x + -16x2 + -8 + -30x + 16x2 Reorder the terms: -8 + -29x + 16x2 = 8 + -8 + 30x + -30x + -16x2 + 16x2 Combine like terms: 8 + -8 = 0 -8 + -29x + 16x2 = 0 + 30x + -30x + -16x2 + 16x2 -8 + -29x + 16x2 = 30x + -30x + -16x2 + 16x2 Combine like terms: 30x + -30x = 0 -8 + -29x + 16x2 = 0 + -16x2 + 16x2 -8 + -29x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -8 + -29x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5 + -1.8125x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.8125x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.8125x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.8125x + x2 = 0 + 0.5 -1.8125x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.8125x + x2 = 0.5 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 = 0.5 + 0.8212890625 Reorder the terms: 0.8212890625 + -1.8125x + x2 = 0.5 + 0.8212890625 Combine like terms: 0.5 + 0.8212890625 = 1.3212890625 0.8212890625 + -1.8125x + x2 = 1.3212890625 Factor a perfect square on the left side: (x + -0.90625)(x + -0.90625) = 1.3212890625 Calculate the square root of the right side: 1.149473385 Break this problem into two subproblems by setting (x + -0.90625) equal to 1.149473385 and -1.149473385.Subproblem 1
x + -0.90625 = 1.149473385 Simplifying x + -0.90625 = 1.149473385 Reorder the terms: -0.90625 + x = 1.149473385 Solving -0.90625 + x = 1.149473385 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 = 1.149473385 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = 1.149473385 + 0.90625 x = 1.149473385 + 0.90625 Combine like terms: 1.149473385 + 0.90625 = 2.055723385 x = 2.055723385 Simplifying x = 2.055723385Subproblem 2
x + -0.90625 = -1.149473385 Simplifying x + -0.90625 = -1.149473385 Reorder the terms: -0.90625 + x = -1.149473385 Solving -0.90625 + x = -1.149473385 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 = -1.149473385 + 0.90625 Combine like terms: -0.90625 + 0.90625 = 0.00000 0.00000 + x = -1.149473385 + 0.90625 x = -1.149473385 + 0.90625 Combine like terms: -1.149473385 + 0.90625 = -0.243223385 x = -0.243223385 Simplifying x = -0.243223385Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.055723385, -0.243223385}
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