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Simplifying 0 = -4x2 + 9x + 3 Reorder the terms: 0 = 3 + 9x + -4x2 Solving 0 = 3 + 9x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -9x + 4x2 = 3 + 9x + -4x2 + -3 + -9x + 4x2 Reorder the terms: -3 + -9x + 4x2 = 3 + -3 + 9x + -9x + -4x2 + 4x2 Combine like terms: 3 + -3 = 0 -3 + -9x + 4x2 = 0 + 9x + -9x + -4x2 + 4x2 -3 + -9x + 4x2 = 9x + -9x + -4x2 + 4x2 Combine like terms: 9x + -9x = 0 -3 + -9x + 4x2 = 0 + -4x2 + 4x2 -3 + -9x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -3 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -2.25x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -2.25x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -2.25x + x2 = 0 + 0.75 -2.25x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -2.25x + x2 = 0.75 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 = 0.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 0.75 + 1.265625 Combine like terms: 0.75 + 1.265625 = 2.015625 1.265625 + -2.25x + x2 = 2.015625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 2.015625 Calculate the square root of the right side: 1.419727086 Break this problem into two subproblems by setting (x + -1.125) equal to 1.419727086 and -1.419727086.Subproblem 1
x + -1.125 = 1.419727086 Simplifying x + -1.125 = 1.419727086 Reorder the terms: -1.125 + x = 1.419727086 Solving -1.125 + x = 1.419727086 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 = 1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 1.419727086 + 1.125 x = 1.419727086 + 1.125 Combine like terms: 1.419727086 + 1.125 = 2.544727086 x = 2.544727086 Simplifying x = 2.544727086Subproblem 2
x + -1.125 = -1.419727086 Simplifying x + -1.125 = -1.419727086 Reorder the terms: -1.125 + x = -1.419727086 Solving -1.125 + x = -1.419727086 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 = -1.419727086 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -1.419727086 + 1.125 x = -1.419727086 + 1.125 Combine like terms: -1.419727086 + 1.125 = -0.294727086 x = -0.294727086 Simplifying x = -0.294727086Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.544727086, -0.294727086}
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