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Simplifying 4x2 + 11x + -300 = 0 Reorder the terms: -300 + 11x + 4x2 = 0 Solving -300 + 11x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -75 + 2.75x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + 2.75x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 2.75x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 2.75x + x2 = 0 + 75 2.75x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 2.75x + x2 = 75 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 75 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 75 + 1.890625 Combine like terms: 75 + 1.890625 = 76.890625 1.890625 + 2.75x + x2 = 76.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 76.890625 Calculate the square root of the right side: 8.768729954 Break this problem into two subproblems by setting (x + 1.375) equal to 8.768729954 and -8.768729954.Subproblem 1
x + 1.375 = 8.768729954 Simplifying x + 1.375 = 8.768729954 Reorder the terms: 1.375 + x = 8.768729954 Solving 1.375 + x = 8.768729954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 8.768729954 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 8.768729954 + -1.375 x = 8.768729954 + -1.375 Combine like terms: 8.768729954 + -1.375 = 7.393729954 x = 7.393729954 Simplifying x = 7.393729954Subproblem 2
x + 1.375 = -8.768729954 Simplifying x + 1.375 = -8.768729954 Reorder the terms: 1.375 + x = -8.768729954 Solving 1.375 + x = -8.768729954 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -8.768729954 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -8.768729954 + -1.375 x = -8.768729954 + -1.375 Combine like terms: -8.768729954 + -1.375 = -10.143729954 x = -10.143729954 Simplifying x = -10.143729954Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.393729954, -10.143729954}
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