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Simplifying 0 = 4x2 + -3x + -9 Reorder the terms: 0 = -9 + -3x + 4x2 Solving 0 = -9 + -3x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + 3x + -4x2 = -9 + -3x + 4x2 + 9 + 3x + -4x2 Reorder the terms: 9 + 3x + -4x2 = -9 + 9 + -3x + 3x + 4x2 + -4x2 Combine like terms: -9 + 9 = 0 9 + 3x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2 9 + 3x + -4x2 = -3x + 3x + 4x2 + -4x2 Combine like terms: -3x + 3x = 0 9 + 3x + -4x2 = 0 + 4x2 + -4x2 9 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 9 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.75x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.75x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.75x + x2 = 0 + 2.25 -0.75x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.75x + x2 = 2.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 2.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 2.25 + 0.140625 Combine like terms: 2.25 + 0.140625 = 2.390625 0.140625 + -0.75x + x2 = 2.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + -0.375) equal to 1.54616461 and -1.54616461.Subproblem 1
x + -0.375 = 1.54616461 Simplifying x + -0.375 = 1.54616461 Reorder the terms: -0.375 + x = 1.54616461 Solving -0.375 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.54616461 + 0.375 x = 1.54616461 + 0.375 Combine like terms: 1.54616461 + 0.375 = 1.92116461 x = 1.92116461 Simplifying x = 1.92116461Subproblem 2
x + -0.375 = -1.54616461 Simplifying x + -0.375 = -1.54616461 Reorder the terms: -0.375 + x = -1.54616461 Solving -0.375 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.54616461 + 0.375 x = -1.54616461 + 0.375 Combine like terms: -1.54616461 + 0.375 = -1.17116461 x = -1.17116461 Simplifying x = -1.17116461Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.92116461, -1.17116461}
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