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Simplifying -16x2 + 12x + 22 = 13.36 Reorder the terms: 22 + 12x + -16x2 = 13.36 Solving 22 + 12x + -16x2 = 13.36 Solving for variable 'x'. Reorder the terms: 22 + -13.36 + 12x + -16x2 = 13.36 + -13.36 Combine like terms: 22 + -13.36 = 8.64 8.64 + 12x + -16x2 = 13.36 + -13.36 Combine like terms: 13.36 + -13.36 = 0.00 8.64 + 12x + -16x2 = 0.00 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.54 + -0.75x + x2 = 0.00 Move the constant term to the right: Add '0.54' to each side of the equation. -0.54 + -0.75x + 0.54 + x2 = 0.00 + 0.54 Reorder the terms: -0.54 + 0.54 + -0.75x + x2 = 0.00 + 0.54 Combine like terms: -0.54 + 0.54 = 0.00 0.00 + -0.75x + x2 = 0.00 + 0.54 -0.75x + x2 = 0.00 + 0.54 Combine like terms: 0.00 + 0.54 = 0.54 -0.75x + x2 = 0.54 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 0.54 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 0.54 + 0.140625 Combine like terms: 0.54 + 0.140625 = 0.680625 0.140625 + -0.75x + x2 = 0.680625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 0.680625 Calculate the square root of the right side: 0.825 Break this problem into two subproblems by setting (x + -0.375) equal to 0.825 and -0.825.Subproblem 1
x + -0.375 = 0.825 Simplifying x + -0.375 = 0.825 Reorder the terms: -0.375 + x = 0.825 Solving -0.375 + x = 0.825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 0.825 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 0.825 + 0.375 x = 0.825 + 0.375 Combine like terms: 0.825 + 0.375 = 1.2 x = 1.2 Simplifying x = 1.2Subproblem 2
x + -0.375 = -0.825 Simplifying x + -0.375 = -0.825 Reorder the terms: -0.375 + x = -0.825 Solving -0.375 + x = -0.825 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -0.825 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -0.825 + 0.375 x = -0.825 + 0.375 Combine like terms: -0.825 + 0.375 = -0.45 x = -0.45 Simplifying x = -0.45Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2, -0.45}
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