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Simplifying -1x2 + 4x = -53 Reorder the terms: 4x + -1x2 = -53 Solving 4x + -1x2 = -53 Solving for variable 'x'. Reorder the terms: 53 + 4x + -1x2 = -53 + 53 Combine like terms: -53 + 53 = 0 53 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -53 + -4x + x2 = 0 Move the constant term to the right: Add '53' to each side of the equation. -53 + -4x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -4x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -4x + x2 = 0 + 53 -4x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -4x + x2 = 53 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 = 53 + 4 Reorder the terms: 4 + -4x + x2 = 53 + 4 Combine like terms: 53 + 4 = 57 4 + -4x + x2 = 57 Factor a perfect square on the left side: (x + -2)(x + -2) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -2) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -2 = 7.549834435 Simplifying x + -2 = 7.549834435 Reorder the terms: -2 + x = 7.549834435 Solving -2 + x = 7.549834435 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 = 7.549834435 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.549834435 + 2 x = 7.549834435 + 2 Combine like terms: 7.549834435 + 2 = 9.549834435 x = 9.549834435 Simplifying x = 9.549834435Subproblem 2
x + -2 = -7.549834435 Simplifying x + -2 = -7.549834435 Reorder the terms: -2 + x = -7.549834435 Solving -2 + x = -7.549834435 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 = -7.549834435 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.549834435 + 2 x = -7.549834435 + 2 Combine like terms: -7.549834435 + 2 = -5.549834435 x = -5.549834435 Simplifying x = -5.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.549834435, -5.549834435}
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