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Simplifying 144x2 + 72x + 9 + -1 = 11 Reorder the terms: 9 + -1 + 72x + 144x2 = 11 Combine like terms: 9 + -1 = 8 8 + 72x + 144x2 = 11 Solving 8 + 72x + 144x2 = 11 Solving for variable 'x'. Reorder the terms: 8 + -11 + 72x + 144x2 = 11 + -11 Combine like terms: 8 + -11 = -3 -3 + 72x + 144x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -3 + 72x + 144x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 24x + 48x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 24x + 48x2)' equal to zero and attempt to solve: Simplifying -1 + 24x + 48x2 = 0 Solving -1 + 24x + 48x2 = 0 Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.02083333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.02083333333' to each side of the equation. -0.02083333333 + 0.5x + 0.02083333333 + x2 = 0 + 0.02083333333 Reorder the terms: -0.02083333333 + 0.02083333333 + 0.5x + x2 = 0 + 0.02083333333 Combine like terms: -0.02083333333 + 0.02083333333 = 0.00000000000 0.00000000000 + 0.5x + x2 = 0 + 0.02083333333 0.5x + x2 = 0 + 0.02083333333 Combine like terms: 0 + 0.02083333333 = 0.02083333333 0.5x + x2 = 0.02083333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.02083333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.02083333333 + 0.0625 Combine like terms: 0.02083333333 + 0.0625 = 0.08333333333 0.0625 + 0.5x + x2 = 0.08333333333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.08333333333 Calculate the square root of the right side: 0.288675135 Break this problem into two subproblems by setting (x + 0.25) equal to 0.288675135 and -0.288675135.Subproblem 1
x + 0.25 = 0.288675135 Simplifying x + 0.25 = 0.288675135 Reorder the terms: 0.25 + x = 0.288675135 Solving 0.25 + x = 0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.288675135 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.288675135 + -0.25 x = 0.288675135 + -0.25 Combine like terms: 0.288675135 + -0.25 = 0.038675135 x = 0.038675135 Simplifying x = 0.038675135Subproblem 2
x + 0.25 = -0.288675135 Simplifying x + 0.25 = -0.288675135 Reorder the terms: 0.25 + x = -0.288675135 Solving 0.25 + x = -0.288675135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.288675135 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.288675135 + -0.25 x = -0.288675135 + -0.25 Combine like terms: -0.288675135 + -0.25 = -0.538675135 x = -0.538675135 Simplifying x = -0.538675135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.038675135, -0.538675135}Solution
x = {0.038675135, -0.538675135}
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