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Simplifying 7x + 22 = x2 Reorder the terms: 22 + 7x = x2 Solving 22 + 7x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 22 + 7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -22 + -7x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -7x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -7x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -7x + x2 = 0 + 22 -7x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -7x + x2 = 22 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 22 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 22 + 12.25 Combine like terms: 22 + 12.25 = 34.25 12.25 + -7x + x2 = 34.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -3.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -3.5 = 5.852349955 Simplifying x + -3.5 = 5.852349955 Reorder the terms: -3.5 + x = 5.852349955 Solving -3.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.852349955 + 3.5 x = 5.852349955 + 3.5 Combine like terms: 5.852349955 + 3.5 = 9.352349955 x = 9.352349955 Simplifying x = 9.352349955Subproblem 2
x + -3.5 = -5.852349955 Simplifying x + -3.5 = -5.852349955 Reorder the terms: -3.5 + x = -5.852349955 Solving -3.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.852349955 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.852349955 + 3.5 x = -5.852349955 + 3.5 Combine like terms: -5.852349955 + 3.5 = -2.352349955 x = -2.352349955 Simplifying x = -2.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.352349955, -2.352349955}
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