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Simplifying 8x2 + 18x + -24 = 9 Reorder the terms: -24 + 18x + 8x2 = 9 Solving -24 + 18x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -24 + -9 + 18x + 8x2 = 9 + -9 Combine like terms: -24 + -9 = -33 -33 + 18x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -33 + 18x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -4.125 + 2.25x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + 2.25x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + 2.25x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + 2.25x + x2 = 0 + 4.125 2.25x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 2.25x + x2 = 4.125 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 = 4.125 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 4.125 + 1.265625 Combine like terms: 4.125 + 1.265625 = 5.390625 1.265625 + 2.25x + x2 = 5.390625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 5.390625 Calculate the square root of the right side: 2.321771953 Break this problem into two subproblems by setting (x + 1.125) equal to 2.321771953 and -2.321771953.Subproblem 1
x + 1.125 = 2.321771953 Simplifying x + 1.125 = 2.321771953 Reorder the terms: 1.125 + x = 2.321771953 Solving 1.125 + x = 2.321771953 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 = 2.321771953 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.321771953 + -1.125 x = 2.321771953 + -1.125 Combine like terms: 2.321771953 + -1.125 = 1.196771953 x = 1.196771953 Simplifying x = 1.196771953Subproblem 2
x + 1.125 = -2.321771953 Simplifying x + 1.125 = -2.321771953 Reorder the terms: 1.125 + x = -2.321771953 Solving 1.125 + x = -2.321771953 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 = -2.321771953 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.321771953 + -1.125 x = -2.321771953 + -1.125 Combine like terms: -2.321771953 + -1.125 = -3.446771953 x = -3.446771953 Simplifying x = -3.446771953Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.196771953, -3.446771953}
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