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Simplifying -16x2 + 16x + 38 = 0 Reorder the terms: 38 + 16x + -16x2 = 0 Solving 38 + 16x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 8x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 8x + -8x2)' equal to zero and attempt to solve: Simplifying 19 + 8x + -8x2 = 0 Solving 19 + 8x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.375 + -1x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -1x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -1x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -1x + x2 = 0 + 2.375 -1x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -1x + x2 = 2.375 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.375 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.375 + 0.25 Combine like terms: 2.375 + 0.25 = 2.625 0.25 + -1x + x2 = 2.625 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (x + -0.5) equal to 1.620185175 and -1.620185175.Subproblem 1
x + -0.5 = 1.620185175 Simplifying x + -0.5 = 1.620185175 Reorder the terms: -0.5 + x = 1.620185175 Solving -0.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.620185175 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.620185175 + 0.5 x = 1.620185175 + 0.5 Combine like terms: 1.620185175 + 0.5 = 2.120185175 x = 2.120185175 Simplifying x = 2.120185175Subproblem 2
x + -0.5 = -1.620185175 Simplifying x + -0.5 = -1.620185175 Reorder the terms: -0.5 + x = -1.620185175 Solving -0.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.620185175 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.620185175 + 0.5 x = -1.620185175 + 0.5 Combine like terms: -1.620185175 + 0.5 = -1.120185175 x = -1.120185175 Simplifying x = -1.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.120185175, -1.120185175}Solution
x = {2.120185175, -1.120185175}
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