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Simplifying -1x2 + 4x = -43 Reorder the terms: 4x + -1x2 = -43 Solving 4x + -1x2 = -43 Solving for variable 'x'. Reorder the terms: 43 + 4x + -1x2 = -43 + 43 Combine like terms: -43 + 43 = 0 43 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -43 + -4x + x2 = 0 Move the constant term to the right: Add '43' to each side of the equation. -43 + -4x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -4x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -4x + x2 = 0 + 43 -4x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -4x + x2 = 43 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 = 43 + 4 Reorder the terms: 4 + -4x + x2 = 43 + 4 Combine like terms: 43 + 4 = 47 4 + -4x + x2 = 47 Factor a perfect square on the left side: (x + -2)(x + -2) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (x + -2) equal to 6.8556546 and -6.8556546.Subproblem 1
x + -2 = 6.8556546 Simplifying x + -2 = 6.8556546 Reorder the terms: -2 + x = 6.8556546 Solving -2 + x = 6.8556546 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 = 6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.8556546 + 2 x = 6.8556546 + 2 Combine like terms: 6.8556546 + 2 = 8.8556546 x = 8.8556546 Simplifying x = 8.8556546Subproblem 2
x + -2 = -6.8556546 Simplifying x + -2 = -6.8556546 Reorder the terms: -2 + x = -6.8556546 Solving -2 + x = -6.8556546 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 = -6.8556546 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.8556546 + 2 x = -6.8556546 + 2 Combine like terms: -6.8556546 + 2 = -4.8556546 x = -4.8556546 Simplifying x = -4.8556546Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.8556546, -4.8556546}
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