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Simplifying 2x2 + 3x + -300 = 0 Reorder the terms: -300 + 3x + 2x2 = 0 Solving -300 + 3x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -150 + 1.5x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 1.5x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 1.5x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 1.5x + x2 = 0 + 150 1.5x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 1.5x + x2 = 150 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 = 150 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 150 + 0.5625 Combine like terms: 150 + 0.5625 = 150.5625 0.5625 + 1.5x + x2 = 150.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 150.5625 Calculate the square root of the right side: 12.270391192 Break this problem into two subproblems by setting (x + 0.75) equal to 12.270391192 and -12.270391192.Subproblem 1
x + 0.75 = 12.270391192 Simplifying x + 0.75 = 12.270391192 Reorder the terms: 0.75 + x = 12.270391192 Solving 0.75 + x = 12.270391192 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 = 12.270391192 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 12.270391192 + -0.75 x = 12.270391192 + -0.75 Combine like terms: 12.270391192 + -0.75 = 11.520391192 x = 11.520391192 Simplifying x = 11.520391192Subproblem 2
x + 0.75 = -12.270391192 Simplifying x + 0.75 = -12.270391192 Reorder the terms: 0.75 + x = -12.270391192 Solving 0.75 + x = -12.270391192 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 = -12.270391192 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -12.270391192 + -0.75 x = -12.270391192 + -0.75 Combine like terms: -12.270391192 + -0.75 = -13.020391192 x = -13.020391192 Simplifying x = -13.020391192Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.520391192, -13.020391192}
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