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Simplifying -1x2 + -4x = -47 Reorder the terms: -4x + -1x2 = -47 Solving -4x + -1x2 = -47 Solving for variable 'x'. Reorder the terms: 47 + -4x + -1x2 = -47 + 47 Combine like terms: -47 + 47 = 0 47 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + 4x + x2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 4x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 4x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 4x + x2 = 0 + 47 4x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 4x + x2 = 47 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 = 47 + 4 Reorder the terms: 4 + 4x + x2 = 47 + 4 Combine like terms: 47 + 4 = 51 4 + 4x + x2 = 51 Factor a perfect square on the left side: (x + 2)(x + 2) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + 2) equal to 7.141428429 and -7.141428429.Subproblem 1
x + 2 = 7.141428429 Simplifying x + 2 = 7.141428429 Reorder the terms: 2 + x = 7.141428429 Solving 2 + x = 7.141428429 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 = 7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + x = 7.141428429 + -2 x = 7.141428429 + -2 Combine like terms: 7.141428429 + -2 = 5.141428429 x = 5.141428429 Simplifying x = 5.141428429Subproblem 2
x + 2 = -7.141428429 Simplifying x + 2 = -7.141428429 Reorder the terms: 2 + x = -7.141428429 Solving 2 + x = -7.141428429 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 = -7.141428429 + -2 Combine like terms: 2 + -2 = 0 0 + x = -7.141428429 + -2 x = -7.141428429 + -2 Combine like terms: -7.141428429 + -2 = -9.141428429 x = -9.141428429 Simplifying x = -9.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.141428429, -9.141428429}
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