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Simplifying -16x2 + 54x + -30 = 0 Reorder the terms: -30 + 54x + -16x2 = 0 Solving -30 + 54x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 27x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + 27x + -8x2)' equal to zero and attempt to solve: Simplifying -15 + 27x + -8x2 = 0 Solving -15 + 27x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.875 + -3.375x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -3.375x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -3.375x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -3.375x + x2 = 0 + -1.875 -3.375x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -3.375x + x2 = -1.875 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = -1.875 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = -1.875 + 2.84765625 Combine like terms: -1.875 + 2.84765625 = 0.97265625 2.84765625 + -3.375x + x2 = 0.97265625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (x + -1.6875) equal to 0.986233365 and -0.986233365.Subproblem 1
x + -1.6875 = 0.986233365 Simplifying x + -1.6875 = 0.986233365 Reorder the terms: -1.6875 + x = 0.986233365 Solving -1.6875 + x = 0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 0.986233365 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 0.986233365 + 1.6875 x = 0.986233365 + 1.6875 Combine like terms: 0.986233365 + 1.6875 = 2.673733365 x = 2.673733365 Simplifying x = 2.673733365Subproblem 2
x + -1.6875 = -0.986233365 Simplifying x + -1.6875 = -0.986233365 Reorder the terms: -1.6875 + x = -0.986233365 Solving -1.6875 + x = -0.986233365 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -0.986233365 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -0.986233365 + 1.6875 x = -0.986233365 + 1.6875 Combine like terms: -0.986233365 + 1.6875 = 0.701266635 x = 0.701266635 Simplifying x = 0.701266635Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.673733365, 0.701266635}Solution
x = {2.673733365, 0.701266635}
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