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Simplifying -16x2 + 42x + 144 = 0 Reorder the terms: 144 + 42x + -16x2 = 0 Solving 144 + 42x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(72 + 21x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(72 + 21x + -8x2)' equal to zero and attempt to solve: Simplifying 72 + 21x + -8x2 = 0 Solving 72 + 21x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -9 + -2.625x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -2.625x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -2.625x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2.625x + x2 = 0 + 9 -2.625x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -2.625x + x2 = 9 The x term is -2.625x. Take half its coefficient (-1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. -2.625x + 1.72265625 + x2 = 9 + 1.72265625 Reorder the terms: 1.72265625 + -2.625x + x2 = 9 + 1.72265625 Combine like terms: 9 + 1.72265625 = 10.72265625 1.72265625 + -2.625x + x2 = 10.72265625 Factor a perfect square on the left side: (x + -1.3125)(x + -1.3125) = 10.72265625 Calculate the square root of the right side: 3.274546724 Break this problem into two subproblems by setting (x + -1.3125) equal to 3.274546724 and -3.274546724.Subproblem 1
x + -1.3125 = 3.274546724 Simplifying x + -1.3125 = 3.274546724 Reorder the terms: -1.3125 + x = 3.274546724 Solving -1.3125 + x = 3.274546724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = 3.274546724 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = 3.274546724 + 1.3125 x = 3.274546724 + 1.3125 Combine like terms: 3.274546724 + 1.3125 = 4.587046724 x = 4.587046724 Simplifying x = 4.587046724Subproblem 2
x + -1.3125 = -3.274546724 Simplifying x + -1.3125 = -3.274546724 Reorder the terms: -1.3125 + x = -3.274546724 Solving -1.3125 + x = -3.274546724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.3125' to each side of the equation. -1.3125 + 1.3125 + x = -3.274546724 + 1.3125 Combine like terms: -1.3125 + 1.3125 = 0.0000 0.0000 + x = -3.274546724 + 1.3125 x = -3.274546724 + 1.3125 Combine like terms: -3.274546724 + 1.3125 = -1.962046724 x = -1.962046724 Simplifying x = -1.962046724Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.587046724, -1.962046724}Solution
x = {4.587046724, -1.962046724}
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