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Simplifying 4x2 + -11x + -7 = 0 Reorder the terms: -7 + -11x + 4x2 = 0 Solving -7 + -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'. -1.75 + -2.75x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -2.75x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -2.75x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -2.75x + x2 = 0 + 1.75 -2.75x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -2.75x + x2 = 1.75 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 = 1.75 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 1.75 + 1.890625 Combine like terms: 1.75 + 1.890625 = 3.640625 1.890625 + -2.75x + x2 = 3.640625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + -1.375) equal to 1.90804219 and -1.90804219.Subproblem 1
x + -1.375 = 1.90804219 Simplifying x + -1.375 = 1.90804219 Reorder the terms: -1.375 + x = 1.90804219 Solving -1.375 + x = 1.90804219 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 = 1.90804219 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.90804219 + 1.375 x = 1.90804219 + 1.375 Combine like terms: 1.90804219 + 1.375 = 3.28304219 x = 3.28304219 Simplifying x = 3.28304219Subproblem 2
x + -1.375 = -1.90804219 Simplifying x + -1.375 = -1.90804219 Reorder the terms: -1.375 + x = -1.90804219 Solving -1.375 + x = -1.90804219 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 = -1.90804219 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.90804219 + 1.375 x = -1.90804219 + 1.375 Combine like terms: -1.90804219 + 1.375 = -0.53304219 x = -0.53304219 Simplifying x = -0.53304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.28304219, -0.53304219}
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