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Simplifying 24x2 + -33x = 18 Reorder the terms: -33x + 24x2 = 18 Solving -33x + 24x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -33x + 24x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -33x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -11x + 8x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -11x + 8x2)' equal to zero and attempt to solve: Simplifying -6 + -11x + 8x2 = 0 Solving -6 + -11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -1.375x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.375x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.375x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.375x + x2 = 0 + 0.75 -1.375x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.375x + x2 = 0.75 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = 0.75 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 0.75 + 0.47265625 Combine like terms: 0.75 + 0.47265625 = 1.22265625 0.47265625 + -1.375x + x2 = 1.22265625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.105737876 and -1.105737876.Subproblem 1
x + -0.6875 = 1.105737876 Simplifying x + -0.6875 = 1.105737876 Reorder the terms: -0.6875 + x = 1.105737876 Solving -0.6875 + x = 1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 1.105737876 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.105737876 + 0.6875 x = 1.105737876 + 0.6875 Combine like terms: 1.105737876 + 0.6875 = 1.793237876 x = 1.793237876 Simplifying x = 1.793237876Subproblem 2
x + -0.6875 = -1.105737876 Simplifying x + -0.6875 = -1.105737876 Reorder the terms: -0.6875 + x = -1.105737876 Solving -0.6875 + x = -1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -1.105737876 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.105737876 + 0.6875 x = -1.105737876 + 0.6875 Combine like terms: -1.105737876 + 0.6875 = -0.418237876 x = -0.418237876 Simplifying x = -0.418237876Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.793237876, -0.418237876}Solution
x = {1.793237876, -0.418237876}
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