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Simplifying -16x2 + 18x + 200 = 0 Reorder the terms: 200 + 18x + -16x2 = 0 Solving 200 + 18x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(100 + 9x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(100 + 9x + -8x2)' equal to zero and attempt to solve: Simplifying 100 + 9x + -8x2 = 0 Solving 100 + 9x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -12.5 + -1.125x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1.125x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1.125x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1.125x + x2 = 0 + 12.5 -1.125x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1.125x + x2 = 12.5 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 = 12.5 + 0.31640625 Reorder the terms: 0.31640625 + -1.125x + x2 = 12.5 + 0.31640625 Combine like terms: 12.5 + 0.31640625 = 12.81640625 0.31640625 + -1.125x + x2 = 12.81640625 Factor a perfect square on the left side: (x + -0.5625)(x + -0.5625) = 12.81640625 Calculate the square root of the right side: 3.580000873 Break this problem into two subproblems by setting (x + -0.5625) equal to 3.580000873 and -3.580000873.Subproblem 1
x + -0.5625 = 3.580000873 Simplifying x + -0.5625 = 3.580000873 Reorder the terms: -0.5625 + x = 3.580000873 Solving -0.5625 + x = 3.580000873 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 = 3.580000873 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 3.580000873 + 0.5625 x = 3.580000873 + 0.5625 Combine like terms: 3.580000873 + 0.5625 = 4.142500873 x = 4.142500873 Simplifying x = 4.142500873Subproblem 2
x + -0.5625 = -3.580000873 Simplifying x + -0.5625 = -3.580000873 Reorder the terms: -0.5625 + x = -3.580000873 Solving -0.5625 + x = -3.580000873 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 = -3.580000873 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -3.580000873 + 0.5625 x = -3.580000873 + 0.5625 Combine like terms: -3.580000873 + 0.5625 = -3.017500873 x = -3.017500873 Simplifying x = -3.017500873Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.142500873, -3.017500873}Solution
x = {4.142500873, -3.017500873}
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