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Simplifying -16x2 + 22.9x + 12 = 0 Reorder the terms: 12 + 22.9x + -16x2 = 0 Solving 12 + 22.9x + -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'. -0.75 + -1.43125x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.43125x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.43125x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.43125x + x2 = 0 + 0.75 -1.43125x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.43125x + x2 = 0.75 The x term is -1.43125x. Take half its coefficient (-0.715625). Square it (0.5121191406) and add it to both sides. Add '0.5121191406' to each side of the equation. -1.43125x + 0.5121191406 + x2 = 0.75 + 0.5121191406 Reorder the terms: 0.5121191406 + -1.43125x + x2 = 0.75 + 0.5121191406 Combine like terms: 0.75 + 0.5121191406 = 1.2621191406 0.5121191406 + -1.43125x + x2 = 1.2621191406 Factor a perfect square on the left side: (x + -0.715625)(x + -0.715625) = 1.2621191406 Calculate the square root of the right side: 1.12344076 Break this problem into two subproblems by setting (x + -0.715625) equal to 1.12344076 and -1.12344076.Subproblem 1
x + -0.715625 = 1.12344076 Simplifying x + -0.715625 = 1.12344076 Reorder the terms: -0.715625 + x = 1.12344076 Solving -0.715625 + x = 1.12344076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.715625' to each side of the equation. -0.715625 + 0.715625 + x = 1.12344076 + 0.715625 Combine like terms: -0.715625 + 0.715625 = 0.000000 0.000000 + x = 1.12344076 + 0.715625 x = 1.12344076 + 0.715625 Combine like terms: 1.12344076 + 0.715625 = 1.83906576 x = 1.83906576 Simplifying x = 1.83906576Subproblem 2
x + -0.715625 = -1.12344076 Simplifying x + -0.715625 = -1.12344076 Reorder the terms: -0.715625 + x = -1.12344076 Solving -0.715625 + x = -1.12344076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.715625' to each side of the equation. -0.715625 + 0.715625 + x = -1.12344076 + 0.715625 Combine like terms: -0.715625 + 0.715625 = 0.000000 0.000000 + x = -1.12344076 + 0.715625 x = -1.12344076 + 0.715625 Combine like terms: -1.12344076 + 0.715625 = -0.40781576 x = -0.40781576 Simplifying x = -0.40781576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.83906576, -0.40781576}
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