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Simplifying -16x2 + 16x + 1362 = 0 Reorder the terms: 1362 + 16x + -16x2 = 0 Solving 1362 + 16x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(681 + 8x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(681 + 8x + -8x2)' equal to zero and attempt to solve: Simplifying 681 + 8x + -8x2 = 0 Solving 681 + 8x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -85.125 + -1x + x2 = 0 Move the constant term to the right: Add '85.125' to each side of the equation. -85.125 + -1x + 85.125 + x2 = 0 + 85.125 Reorder the terms: -85.125 + 85.125 + -1x + x2 = 0 + 85.125 Combine like terms: -85.125 + 85.125 = 0.000 0.000 + -1x + x2 = 0 + 85.125 -1x + x2 = 0 + 85.125 Combine like terms: 0 + 85.125 = 85.125 -1x + x2 = 85.125 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 = 85.125 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 85.125 + 0.25 Combine like terms: 85.125 + 0.25 = 85.375 0.25 + -1x + x2 = 85.375 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 85.375 Calculate the square root of the right side: 9.239859306 Break this problem into two subproblems by setting (x + -0.5) equal to 9.239859306 and -9.239859306.Subproblem 1
x + -0.5 = 9.239859306 Simplifying x + -0.5 = 9.239859306 Reorder the terms: -0.5 + x = 9.239859306 Solving -0.5 + x = 9.239859306 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 = 9.239859306 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.239859306 + 0.5 x = 9.239859306 + 0.5 Combine like terms: 9.239859306 + 0.5 = 9.739859306 x = 9.739859306 Simplifying x = 9.739859306Subproblem 2
x + -0.5 = -9.239859306 Simplifying x + -0.5 = -9.239859306 Reorder the terms: -0.5 + x = -9.239859306 Solving -0.5 + x = -9.239859306 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 = -9.239859306 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.239859306 + 0.5 x = -9.239859306 + 0.5 Combine like terms: -9.239859306 + 0.5 = -8.739859306 x = -8.739859306 Simplifying x = -8.739859306Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.739859306, -8.739859306}Solution
x = {9.739859306, -8.739859306}
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