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Simplifying 16x2 + 18x + -2196 = 0 Reorder the terms: -2196 + 18x + 16x2 = 0 Solving -2196 + 18x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1098 + 9x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1098 + 9x + 8x2)' equal to zero and attempt to solve: Simplifying -1098 + 9x + 8x2 = 0 Solving -1098 + 9x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -137.25 + 1.125x + x2 = 0 Move the constant term to the right: Add '137.25' to each side of the equation. -137.25 + 1.125x + 137.25 + x2 = 0 + 137.25 Reorder the terms: -137.25 + 137.25 + 1.125x + x2 = 0 + 137.25 Combine like terms: -137.25 + 137.25 = 0.00 0.00 + 1.125x + x2 = 0 + 137.25 1.125x + x2 = 0 + 137.25 Combine like terms: 0 + 137.25 = 137.25 1.125x + x2 = 137.25 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 = 137.25 + 0.31640625 Reorder the terms: 0.31640625 + 1.125x + x2 = 137.25 + 0.31640625 Combine like terms: 137.25 + 0.31640625 = 137.56640625 0.31640625 + 1.125x + x2 = 137.56640625 Factor a perfect square on the left side: (x + 0.5625)(x + 0.5625) = 137.56640625 Calculate the square root of the right side: 11.72887063 Break this problem into two subproblems by setting (x + 0.5625) equal to 11.72887063 and -11.72887063.Subproblem 1
x + 0.5625 = 11.72887063 Simplifying x + 0.5625 = 11.72887063 Reorder the terms: 0.5625 + x = 11.72887063 Solving 0.5625 + x = 11.72887063 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 = 11.72887063 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = 11.72887063 + -0.5625 x = 11.72887063 + -0.5625 Combine like terms: 11.72887063 + -0.5625 = 11.16637063 x = 11.16637063 Simplifying x = 11.16637063Subproblem 2
x + 0.5625 = -11.72887063 Simplifying x + 0.5625 = -11.72887063 Reorder the terms: 0.5625 + x = -11.72887063 Solving 0.5625 + x = -11.72887063 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 = -11.72887063 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + x = -11.72887063 + -0.5625 x = -11.72887063 + -0.5625 Combine like terms: -11.72887063 + -0.5625 = -12.29137063 x = -12.29137063 Simplifying x = -12.29137063Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.16637063, -12.29137063}Solution
x = {11.16637063, -12.29137063}
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