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Simplifying 4x2 + 9x + -69 = 0 Reorder the terms: -69 + 9x + 4x2 = 0 Solving -69 + 9x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -17.25 + 2.25x + x2 = 0 Move the constant term to the right: Add '17.25' to each side of the equation. -17.25 + 2.25x + 17.25 + x2 = 0 + 17.25 Reorder the terms: -17.25 + 17.25 + 2.25x + x2 = 0 + 17.25 Combine like terms: -17.25 + 17.25 = 0.00 0.00 + 2.25x + x2 = 0 + 17.25 2.25x + x2 = 0 + 17.25 Combine like terms: 0 + 17.25 = 17.25 2.25x + x2 = 17.25 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 = 17.25 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 17.25 + 1.265625 Combine like terms: 17.25 + 1.265625 = 18.515625 1.265625 + 2.25x + x2 = 18.515625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 18.515625 Calculate the square root of the right side: 4.30297862 Break this problem into two subproblems by setting (x + 1.125) equal to 4.30297862 and -4.30297862.Subproblem 1
x + 1.125 = 4.30297862 Simplifying x + 1.125 = 4.30297862 Reorder the terms: 1.125 + x = 4.30297862 Solving 1.125 + x = 4.30297862 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 = 4.30297862 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 4.30297862 + -1.125 x = 4.30297862 + -1.125 Combine like terms: 4.30297862 + -1.125 = 3.17797862 x = 3.17797862 Simplifying x = 3.17797862Subproblem 2
x + 1.125 = -4.30297862 Simplifying x + 1.125 = -4.30297862 Reorder the terms: 1.125 + x = -4.30297862 Solving 1.125 + x = -4.30297862 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 = -4.30297862 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -4.30297862 + -1.125 x = -4.30297862 + -1.125 Combine like terms: -4.30297862 + -1.125 = -5.42797862 x = -5.42797862 Simplifying x = -5.42797862Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.17797862, -5.42797862}
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