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Simplifying 0 = -16x2 + 36x + 4 Reorder the terms: 0 = 4 + 36x + -16x2 Solving 0 = 4 + 36x + -16x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -36x + 16x2 = 4 + 36x + -16x2 + -4 + -36x + 16x2 Reorder the terms: -4 + -36x + 16x2 = 4 + -4 + 36x + -36x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -36x + 16x2 = 0 + 36x + -36x + -16x2 + 16x2 -4 + -36x + 16x2 = 36x + -36x + -16x2 + 16x2 Combine like terms: 36x + -36x = 0 -4 + -36x + 16x2 = 0 + -16x2 + 16x2 -4 + -36x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -36x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + -9x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -9x + 4x2)' equal to zero and attempt to solve: Simplifying -1 + -9x + 4x2 = 0 Solving -1 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.25x + x2 = 0 + 0.25 -2.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.25x + x2 = 0.25 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 0.25 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.25 + 1.265625 Combine like terms: 0.25 + 1.265625 = 1.515625 1.265625 + -2.25x + x2 = 1.515625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (x + -1.125) equal to 1.231107225 and -1.231107225.Subproblem 1
x + -1.125 = 1.231107225 Simplifying x + -1.125 = 1.231107225 Reorder the terms: -1.125 + x = 1.231107225 Solving -1.125 + x = 1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.231107225 + 1.125 x = 1.231107225 + 1.125 Combine like terms: 1.231107225 + 1.125 = 2.356107225 x = 2.356107225 Simplifying x = 2.356107225Subproblem 2
x + -1.125 = -1.231107225 Simplifying x + -1.125 = -1.231107225 Reorder the terms: -1.125 + x = -1.231107225 Solving -1.125 + x = -1.231107225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -1.231107225 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.231107225 + 1.125 x = -1.231107225 + 1.125 Combine like terms: -1.231107225 + 1.125 = -0.106107225 x = -0.106107225 Simplifying x = -0.106107225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.356107225, -0.106107225}Solution
x = {2.356107225, -0.106107225}
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