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Simplifying -16x2 + 10x + 30 = 0 Reorder the terms: 30 + 10x + -16x2 = 0 Solving 30 + 10x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 5x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 5x + -8x2)' equal to zero and attempt to solve: Simplifying 15 + 5x + -8x2 = 0 Solving 15 + 5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.875 + -0.625x + x2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -0.625x + 1.875 + x2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -0.625x + x2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -0.625x + x2 = 0 + 1.875 -0.625x + x2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -0.625x + x2 = 1.875 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 1.875 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 1.875 + 0.09765625 Combine like terms: 1.875 + 0.09765625 = 1.97265625 0.09765625 + -0.625x + x2 = 1.97265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 1.97265625 Calculate the square root of the right side: 1.404512816 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.404512816 and -1.404512816.Subproblem 1
x + -0.3125 = 1.404512816 Simplifying x + -0.3125 = 1.404512816 Reorder the terms: -0.3125 + x = 1.404512816 Solving -0.3125 + x = 1.404512816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.404512816 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.404512816 + 0.3125 x = 1.404512816 + 0.3125 Combine like terms: 1.404512816 + 0.3125 = 1.717012816 x = 1.717012816 Simplifying x = 1.717012816Subproblem 2
x + -0.3125 = -1.404512816 Simplifying x + -0.3125 = -1.404512816 Reorder the terms: -0.3125 + x = -1.404512816 Solving -0.3125 + x = -1.404512816 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.404512816 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.404512816 + 0.3125 x = -1.404512816 + 0.3125 Combine like terms: -1.404512816 + 0.3125 = -1.092012816 x = -1.092012816 Simplifying x = -1.092012816Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.717012816, -1.092012816}Solution
x = {1.717012816, -1.092012816}
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