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Simplifying 8x2 + 18x + -24 = 0 Reorder the terms: -24 + 18x + 8x2 = 0 Solving -24 + 18x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 9x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 9x + 4x2)' equal to zero and attempt to solve: Simplifying -12 + 9x + 4x2 = 0 Solving -12 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3 + 2.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2.25x + x2 = 0 + 3 2.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2.25x + x2 = 3 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 = 3 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 3 + 1.265625 Combine like terms: 3 + 1.265625 = 4.265625 1.265625 + 2.25x + x2 = 4.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (x + 1.125) equal to 2.065338955 and -2.065338955.Subproblem 1
x + 1.125 = 2.065338955 Simplifying x + 1.125 = 2.065338955 Reorder the terms: 1.125 + x = 2.065338955 Solving 1.125 + x = 2.065338955 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 = 2.065338955 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.065338955 + -1.125 x = 2.065338955 + -1.125 Combine like terms: 2.065338955 + -1.125 = 0.940338955 x = 0.940338955 Simplifying x = 0.940338955Subproblem 2
x + 1.125 = -2.065338955 Simplifying x + 1.125 = -2.065338955 Reorder the terms: 1.125 + x = -2.065338955 Solving 1.125 + x = -2.065338955 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 = -2.065338955 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.065338955 + -1.125 x = -2.065338955 + -1.125 Combine like terms: -2.065338955 + -1.125 = -3.190338955 x = -3.190338955 Simplifying x = -3.190338955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.940338955, -3.190338955}Solution
x = {0.940338955, -3.190338955}
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