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Simplifying -16x2 + 40x + 6 = 0 Reorder the terms: 6 + 40x + -16x2 = 0 Solving 6 + 40x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 20x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 20x + -8x2)' equal to zero and attempt to solve: Simplifying 3 + 20x + -8x2 = 0 Solving 3 + 20x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -2.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -2.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -2.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -2.5x + x2 = 0 + 0.375 -2.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -2.5x + x2 = 0.375 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 0.375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 0.375 + 1.5625 Combine like terms: 0.375 + 1.5625 = 1.9375 1.5625 + -2.5x + x2 = 1.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 1.9375 Calculate the square root of the right side: 1.391941091 Break this problem into two subproblems by setting (x + -1.25) equal to 1.391941091 and -1.391941091.Subproblem 1
x + -1.25 = 1.391941091 Simplifying x + -1.25 = 1.391941091 Reorder the terms: -1.25 + x = 1.391941091 Solving -1.25 + x = 1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 1.391941091 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 1.391941091 + 1.25 x = 1.391941091 + 1.25 Combine like terms: 1.391941091 + 1.25 = 2.641941091 x = 2.641941091 Simplifying x = 2.641941091Subproblem 2
x + -1.25 = -1.391941091 Simplifying x + -1.25 = -1.391941091 Reorder the terms: -1.25 + x = -1.391941091 Solving -1.25 + x = -1.391941091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -1.391941091 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -1.391941091 + 1.25 x = -1.391941091 + 1.25 Combine like terms: -1.391941091 + 1.25 = -0.141941091 x = -0.141941091 Simplifying x = -0.141941091Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.641941091, -0.141941091}Solution
x = {2.641941091, -0.141941091}
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