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Simplifying 16x2 + -18x + -6 = 0 Reorder the terms: -6 + -18x + 16x2 = 0 Solving -6 + -18x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + -9x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -9x + 8x2)' equal to zero and attempt to solve: Simplifying -3 + -9x + 8x2 = 0 Solving -3 + -9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.375 + -1.125x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -1.125x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -1.125x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -1.125x + x2 = 0 + 0.375 -1.125x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -1.125x + x2 = 0.375 The x term is -1.125x. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125x + 0.31640625 + x2 = 0.375 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 0.375 + 0.31640625 Combine like terms: 0.375 + 0.31640625 = 0.69140625 0.31640625 + -1.125x + x2 = 0.69140625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 0.69140625 Calculate the square root of the right side: 0.831508418 Break this problem into two subproblems by setting (x + -0.5625) equal to 0.831508418 and -0.831508418.Subproblem 1
x + -0.5625 = 0.831508418 Simplifying x + -0.5625 = 0.831508418 Reorder the terms: -0.5625 + x = 0.831508418 Solving -0.5625 + x = 0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.831508418 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.831508418 + 0.5625 x = 0.831508418 + 0.5625 Combine like terms: 0.831508418 + 0.5625 = 1.394008418 x = 1.394008418 Simplifying x = 1.394008418Subproblem 2
x + -0.5625 = -0.831508418 Simplifying x + -0.5625 = -0.831508418 Reorder the terms: -0.5625 + x = -0.831508418 Solving -0.5625 + x = -0.831508418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.831508418 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.831508418 + 0.5625 x = -0.831508418 + 0.5625 Combine like terms: -0.831508418 + 0.5625 = -0.269008418 x = -0.269008418 Simplifying x = -0.269008418Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.394008418, -0.269008418}Solution
x = {1.394008418, -0.269008418}
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