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Simplifying -16x2 + -29x + 4 = 16 Reorder the terms: 4 + -29x + -16x2 = 16 Solving 4 + -29x + -16x2 = 16 Solving for variable 'x'. Reorder the terms: 4 + -16 + -29x + -16x2 = 16 + -16 Combine like terms: 4 + -16 = -12 -12 + -29x + -16x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -12 + -29x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 29x + 16x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 29x + 16x2)' equal to zero and attempt to solve: Simplifying 12 + 29x + 16x2 = 0 Solving 12 + 29x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.75 + 1.8125x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 1.8125x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 1.8125x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 1.8125x + x2 = 0 + -0.75 1.8125x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 1.8125x + x2 = -0.75 The x term is 1.8125x. Take half its coefficient (0.90625). Square it (0.8212890625) and add it to both sides. Add '0.8212890625' to each side of the equation. 1.8125x + 0.8212890625 + x2 = -0.75 + 0.8212890625 Reorder the terms: 0.8212890625 + 1.8125x + x2 = -0.75 + 0.8212890625 Combine like terms: -0.75 + 0.8212890625 = 0.0712890625 0.8212890625 + 1.8125x + x2 = 0.0712890625 Factor a perfect square on the left side: (x + 0.90625)(x + 0.90625) = 0.0712890625 Calculate the square root of the right side: 0.267000117 Break this problem into two subproblems by setting (x + 0.90625) equal to 0.267000117 and -0.267000117.Subproblem 1
x + 0.90625 = 0.267000117 Simplifying x + 0.90625 = 0.267000117 Reorder the terms: 0.90625 + x = 0.267000117 Solving 0.90625 + x = 0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = 0.267000117 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = 0.267000117 + -0.90625 x = 0.267000117 + -0.90625 Combine like terms: 0.267000117 + -0.90625 = -0.639249883 x = -0.639249883 Simplifying x = -0.639249883Subproblem 2
x + 0.90625 = -0.267000117 Simplifying x + 0.90625 = -0.267000117 Reorder the terms: 0.90625 + x = -0.267000117 Solving 0.90625 + x = -0.267000117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.90625' to each side of the equation. 0.90625 + -0.90625 + x = -0.267000117 + -0.90625 Combine like terms: 0.90625 + -0.90625 = 0.00000 0.00000 + x = -0.267000117 + -0.90625 x = -0.267000117 + -0.90625 Combine like terms: -0.267000117 + -0.90625 = -1.173250117 x = -1.173250117 Simplifying x = -1.173250117Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.639249883, -1.173250117}Solution
x = {-0.639249883, -1.173250117}
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