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Simplifying 0 = 2x2 + 3x + -7.25 Reorder the terms: 0 = -7.25 + 3x + 2x2 Solving 0 = -7.25 + 3x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 7.25 = 7.25 7.25 + -3x + -2x2 = -7.25 + 3x + 2x2 + 7.25 + -3x + -2x2 Reorder the terms: 7.25 + -3x + -2x2 = -7.25 + 7.25 + 3x + -3x + 2x2 + -2x2 Combine like terms: -7.25 + 7.25 = 0.00 7.25 + -3x + -2x2 = 0.00 + 3x + -3x + 2x2 + -2x2 7.25 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2 Combine like terms: 3x + -3x = 0 7.25 + -3x + -2x2 = 0 + 2x2 + -2x2 7.25 + -3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7.25 + -3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -3.625 + 1.5x + x2 = 0 Move the constant term to the right: Add '3.625' to each side of the equation. -3.625 + 1.5x + 3.625 + x2 = 0 + 3.625 Reorder the terms: -3.625 + 3.625 + 1.5x + x2 = 0 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + 1.5x + x2 = 0 + 3.625 1.5x + x2 = 0 + 3.625 Combine like terms: 0 + 3.625 = 3.625 1.5x + x2 = 3.625 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 = 3.625 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 3.625 + 0.5625 Combine like terms: 3.625 + 0.5625 = 4.1875 0.5625 + 1.5x + x2 = 4.1875 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 4.1875 Calculate the square root of the right side: 2.046338193 Break this problem into two subproblems by setting (x + 0.75) equal to 2.046338193 and -2.046338193.Subproblem 1
x + 0.75 = 2.046338193 Simplifying x + 0.75 = 2.046338193 Reorder the terms: 0.75 + x = 2.046338193 Solving 0.75 + x = 2.046338193 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 = 2.046338193 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.046338193 + -0.75 x = 2.046338193 + -0.75 Combine like terms: 2.046338193 + -0.75 = 1.296338193 x = 1.296338193 Simplifying x = 1.296338193Subproblem 2
x + 0.75 = -2.046338193 Simplifying x + 0.75 = -2.046338193 Reorder the terms: 0.75 + x = -2.046338193 Solving 0.75 + x = -2.046338193 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 = -2.046338193 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.046338193 + -0.75 x = -2.046338193 + -0.75 Combine like terms: -2.046338193 + -0.75 = -2.796338193 x = -2.796338193 Simplifying x = -2.796338193Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.296338193, -2.796338193}
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