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Simplifying -20x + 36 + -32x2 = 0 Reorder the terms: 36 + -20x + -32x2 = 0 Solving 36 + -20x + -32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(9 + -5x + -8x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(9 + -5x + -8x2)' equal to zero and attempt to solve: Simplifying 9 + -5x + -8x2 = 0 Solving 9 + -5x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + 0.625x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.625x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.625x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.625x + x2 = 0 + 1.125 0.625x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.625x + x2 = 1.125 The x term is 0.625x. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x + 0.09765625 + x2 = 1.125 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 1.125 + 0.09765625 Combine like terms: 1.125 + 0.09765625 = 1.22265625 0.09765625 + 0.625x + x2 = 1.22265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (x + 0.3125) equal to 1.105737876 and -1.105737876.Subproblem 1
x + 0.3125 = 1.105737876 Simplifying x + 0.3125 = 1.105737876 Reorder the terms: 0.3125 + x = 1.105737876 Solving 0.3125 + x = 1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = 1.105737876 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 1.105737876 + -0.3125 x = 1.105737876 + -0.3125 Combine like terms: 1.105737876 + -0.3125 = 0.793237876 x = 0.793237876 Simplifying x = 0.793237876Subproblem 2
x + 0.3125 = -1.105737876 Simplifying x + 0.3125 = -1.105737876 Reorder the terms: 0.3125 + x = -1.105737876 Solving 0.3125 + x = -1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x = -1.105737876 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -1.105737876 + -0.3125 x = -1.105737876 + -0.3125 Combine like terms: -1.105737876 + -0.3125 = -1.418237876 x = -1.418237876 Simplifying x = -1.418237876Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.793237876, -1.418237876}Solution
x = {0.793237876, -1.418237876}
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