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Simplifying -16x2 + 33x + 10 = 0 Reorder the terms: 10 + 33x + -16x2 = 0 Solving 10 + 33x + -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'. -0.625 + -2.0625x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -2.0625x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -2.0625x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -2.0625x + x2 = 0 + 0.625 -2.0625x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -2.0625x + x2 = 0.625 The x term is -2.0625x. Take half its coefficient (-1.03125). Square it (1.063476563) and add it to both sides. Add '1.063476563' to each side of the equation. -2.0625x + 1.063476563 + x2 = 0.625 + 1.063476563 Reorder the terms: 1.063476563 + -2.0625x + x2 = 0.625 + 1.063476563 Combine like terms: 0.625 + 1.063476563 = 1.688476563 1.063476563 + -2.0625x + x2 = 1.688476563 Factor a perfect square on the left side: (x + -1.03125)(x + -1.03125) = 1.688476563 Calculate the square root of the right side: 1.299413931 Break this problem into two subproblems by setting (x + -1.03125) equal to 1.299413931 and -1.299413931.Subproblem 1
x + -1.03125 = 1.299413931 Simplifying x + -1.03125 = 1.299413931 Reorder the terms: -1.03125 + x = 1.299413931 Solving -1.03125 + x = 1.299413931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + x = 1.299413931 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = 1.299413931 + 1.03125 x = 1.299413931 + 1.03125 Combine like terms: 1.299413931 + 1.03125 = 2.330663931 x = 2.330663931 Simplifying x = 2.330663931Subproblem 2
x + -1.03125 = -1.299413931 Simplifying x + -1.03125 = -1.299413931 Reorder the terms: -1.03125 + x = -1.299413931 Solving -1.03125 + x = -1.299413931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.03125' to each side of the equation. -1.03125 + 1.03125 + x = -1.299413931 + 1.03125 Combine like terms: -1.03125 + 1.03125 = 0.00000 0.00000 + x = -1.299413931 + 1.03125 x = -1.299413931 + 1.03125 Combine like terms: -1.299413931 + 1.03125 = -0.268163931 x = -0.268163931 Simplifying x = -0.268163931Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.330663931, -0.268163931}
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