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Simplifying 0 = -4x2 + 6x + 9 Reorder the terms: 0 = 9 + 6x + -4x2 Solving 0 = 9 + 6x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -6x + 4x2 = 9 + 6x + -4x2 + -9 + -6x + 4x2 Reorder the terms: -9 + -6x + 4x2 = 9 + -9 + 6x + -6x + -4x2 + 4x2 Combine like terms: 9 + -9 = 0 -9 + -6x + 4x2 = 0 + 6x + -6x + -4x2 + 4x2 -9 + -6x + 4x2 = 6x + -6x + -4x2 + 4x2 Combine like terms: 6x + -6x = 0 -9 + -6x + 4x2 = 0 + -4x2 + 4x2 -9 + -6x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -9 + -6x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -1.5x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -1.5x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -1.5x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -1.5x + x2 = 0 + 2.25 -1.5x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -1.5x + x2 = 2.25 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 2.25 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 2.25 + 0.5625 Combine like terms: 2.25 + 0.5625 = 2.8125 0.5625 + -1.5x + x2 = 2.8125 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 2.8125 Calculate the square root of the right side: 1.677050983 Break this problem into two subproblems by setting (x + -0.75) equal to 1.677050983 and -1.677050983.Subproblem 1
x + -0.75 = 1.677050983 Simplifying x + -0.75 = 1.677050983 Reorder the terms: -0.75 + x = 1.677050983 Solving -0.75 + x = 1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.677050983 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.677050983 + 0.75 x = 1.677050983 + 0.75 Combine like terms: 1.677050983 + 0.75 = 2.427050983 x = 2.427050983 Simplifying x = 2.427050983Subproblem 2
x + -0.75 = -1.677050983 Simplifying x + -0.75 = -1.677050983 Reorder the terms: -0.75 + x = -1.677050983 Solving -0.75 + x = -1.677050983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.677050983 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.677050983 + 0.75 x = -1.677050983 + 0.75 Combine like terms: -1.677050983 + 0.75 = -0.927050983 x = -0.927050983 Simplifying x = -0.927050983Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.427050983, -0.927050983}
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