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Simplifying -1((x2) + -4x + -5) = 7 -1(x2 + -4x + -5) = 7 Reorder the terms: -1(-5 + -4x + x2) = 7 (-5 * -1 + -4x * -1 + x2 * -1) = 7 (5 + 4x + -1x2) = 7 Solving 5 + 4x + -1x2 = 7 Solving for variable 'x'. Reorder the terms: 5 + -7 + 4x + -1x2 = 7 + -7 Combine like terms: 5 + -7 = -2 -2 + 4x + -1x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -2 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -4x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4x + x2 = 0 + -2 -4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4x + x2 = -2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2 + 4 Reorder the terms: 4 + -4x + x2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4x + x2 = 2 Factor a perfect square on the left side: (x + -2)(x + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -2 = 1.414213562 Simplifying x + -2 = 1.414213562 Reorder the terms: -2 + x = 1.414213562 Solving -2 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.414213562 + 2 x = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 x = 3.414213562 Simplifying x = 3.414213562Subproblem 2
x + -2 = -1.414213562 Simplifying x + -2 = -1.414213562 Reorder the terms: -2 + x = -1.414213562 Solving -2 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.414213562 + 2 x = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 x = 0.585786438 Simplifying x = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.414213562, 0.585786438}
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