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Simplifying (4x2) + -1(3x + -5) = 20 Reorder the terms: (4x2) + -1(-5 + 3x) = 20 (4x2) + (-5 * -1 + 3x * -1) = 20 (4x2) + (5 + -3x) = 20 Reorder the terms: 5 + -3x + (4x2) = 20 Solving 5 + -3x + (4x2) = 20 Solving for variable 'x'. Reorder the terms: 5 + -20 + -3x + (4x2) = 20 + -20 Combine like terms: 5 + -20 = -15 -15 + -3x + (4x2) = 20 + -20 Combine like terms: 20 + -20 = 0 -15 + -3x + (4x2) = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -0.75x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -0.75x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -0.75x + x2 = 0 + 3.75 -0.75x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -0.75x + x2 = 3.75 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 = 3.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 3.75 + 0.140625 Combine like terms: 3.75 + 0.140625 = 3.890625 0.140625 + -0.75x + x2 = 3.890625 Factor a perfect square on the left side: ((x) + -0.375)((x) + -0.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting ((x) + -0.375) equal to 1.97246673 and -1.97246673.Subproblem 1
(x) + -0.375 = 1.97246673 Simplifying (x) + -0.375 = 1.97246673 x + -0.375 = 1.97246673 Reorder the terms: -0.375 + x = 1.97246673 Solving -0.375 + x = 1.97246673 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 = 1.97246673 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.97246673 + 0.375 x = 1.97246673 + 0.375 Combine like terms: 1.97246673 + 0.375 = 2.34746673 x = 2.34746673 Simplifying x = 2.34746673Subproblem 2
(x) + -0.375 = -1.97246673 Simplifying (x) + -0.375 = -1.97246673 x + -0.375 = -1.97246673 Reorder the terms: -0.375 + x = -1.97246673 Solving -0.375 + x = -1.97246673 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 = -1.97246673 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.97246673 + 0.375 x = -1.97246673 + 0.375 Combine like terms: -1.97246673 + 0.375 = -1.59746673 x = -1.59746673 Simplifying x = -1.59746673Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.34746673, -1.59746673}
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