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Simplifying 0 = 12 + 105x + 16x2 Solving 0 = 12 + 105x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + -105x + -16x2 = 12 + 105x + 16x2 + -12 + -105x + -16x2 Reorder the terms: -12 + -105x + -16x2 = 12 + -12 + 105x + -105x + 16x2 + -16x2 Combine like terms: 12 + -12 = 0 -12 + -105x + -16x2 = 0 + 105x + -105x + 16x2 + -16x2 -12 + -105x + -16x2 = 105x + -105x + 16x2 + -16x2 Combine like terms: 105x + -105x = 0 -12 + -105x + -16x2 = 0 + 16x2 + -16x2 -12 + -105x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -12 + -105x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 105x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 105x + 16x2)' equal to zero and attempt to solve: Simplifying 12 + 105x + 16x2 = 0 Solving 12 + 105x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.75 + 6.5625x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 6.5625x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 6.5625x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 6.5625x + x2 = 0 + -0.75 6.5625x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 6.5625x + x2 = -0.75 The x term is 6.5625x. Take half its coefficient (3.28125). Square it (10.76660156) and add it to both sides. Add '10.76660156' to each side of the equation. 6.5625x + 10.76660156 + x2 = -0.75 + 10.76660156 Reorder the terms: 10.76660156 + 6.5625x + x2 = -0.75 + 10.76660156 Combine like terms: -0.75 + 10.76660156 = 10.01660156 10.76660156 + 6.5625x + x2 = 10.01660156 Factor a perfect square on the left side: (x + 3.28125)(x + 3.28125) = 10.01660156 Calculate the square root of the right side: 3.164901509 Break this problem into two subproblems by setting (x + 3.28125) equal to 3.164901509 and -3.164901509.Subproblem 1
x + 3.28125 = 3.164901509 Simplifying x + 3.28125 = 3.164901509 Reorder the terms: 3.28125 + x = 3.164901509 Solving 3.28125 + x = 3.164901509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.28125' to each side of the equation. 3.28125 + -3.28125 + x = 3.164901509 + -3.28125 Combine like terms: 3.28125 + -3.28125 = 0.00000 0.00000 + x = 3.164901509 + -3.28125 x = 3.164901509 + -3.28125 Combine like terms: 3.164901509 + -3.28125 = -0.116348491 x = -0.116348491 Simplifying x = -0.116348491Subproblem 2
x + 3.28125 = -3.164901509 Simplifying x + 3.28125 = -3.164901509 Reorder the terms: 3.28125 + x = -3.164901509 Solving 3.28125 + x = -3.164901509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.28125' to each side of the equation. 3.28125 + -3.28125 + x = -3.164901509 + -3.28125 Combine like terms: 3.28125 + -3.28125 = 0.00000 0.00000 + x = -3.164901509 + -3.28125 x = -3.164901509 + -3.28125 Combine like terms: -3.164901509 + -3.28125 = -6.446151509 x = -6.446151509 Simplifying x = -6.446151509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.116348491, -6.446151509}Solution
x = {-0.116348491, -6.446151509}
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