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Simplifying 16x2 + 6x + -100 = 0 Reorder the terms: -100 + 6x + 16x2 = 0 Solving -100 + 6x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 3x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 3x + 8x2)' equal to zero and attempt to solve: Simplifying -50 + 3x + 8x2 = 0 Solving -50 + 3x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.25 + 0.375x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 0.375x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 0.375x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 0.375x + x2 = 0 + 6.25 0.375x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 0.375x + x2 = 6.25 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 6.25 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 6.25 + 0.03515625 Combine like terms: 6.25 + 0.03515625 = 6.28515625 0.03515625 + 0.375x + x2 = 6.28515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 6.28515625 Calculate the square root of the right side: 2.50702139 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.50702139 and -2.50702139.Subproblem 1
x + 0.1875 = 2.50702139 Simplifying x + 0.1875 = 2.50702139 Reorder the terms: 0.1875 + x = 2.50702139 Solving 0.1875 + x = 2.50702139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.50702139 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.50702139 + -0.1875 x = 2.50702139 + -0.1875 Combine like terms: 2.50702139 + -0.1875 = 2.31952139 x = 2.31952139 Simplifying x = 2.31952139Subproblem 2
x + 0.1875 = -2.50702139 Simplifying x + 0.1875 = -2.50702139 Reorder the terms: 0.1875 + x = -2.50702139 Solving 0.1875 + x = -2.50702139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.50702139 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.50702139 + -0.1875 x = -2.50702139 + -0.1875 Combine like terms: -2.50702139 + -0.1875 = -2.69452139 x = -2.69452139 Simplifying x = -2.69452139Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31952139, -2.69452139}Solution
x = {2.31952139, -2.69452139}
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