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Simplifying 5x2 + 22x = 600 Reorder the terms: 22x + 5x2 = 600 Solving 22x + 5x2 = 600 Solving for variable 'x'. Reorder the terms: -600 + 22x + 5x2 = 600 + -600 Combine like terms: 600 + -600 = 0 -600 + 22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -120 + 4.4x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 4.4x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 4.4x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 4.4x + x2 = 0 + 120 4.4x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 4.4x + x2 = 120 The x term is 4.4x. Take half its coefficient (2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. 4.4x + 4.84 + x2 = 120 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 120 + 4.84 Combine like terms: 120 + 4.84 = 124.84 4.84 + 4.4x + x2 = 124.84 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 124.84 Calculate the square root of the right side: 11.173182179 Break this problem into two subproblems by setting (x + 2.2) equal to 11.173182179 and -11.173182179.Subproblem 1
x + 2.2 = 11.173182179 Simplifying x + 2.2 = 11.173182179 Reorder the terms: 2.2 + x = 11.173182179 Solving 2.2 + x = 11.173182179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 11.173182179 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 11.173182179 + -2.2 x = 11.173182179 + -2.2 Combine like terms: 11.173182179 + -2.2 = 8.973182179 x = 8.973182179 Simplifying x = 8.973182179Subproblem 2
x + 2.2 = -11.173182179 Simplifying x + 2.2 = -11.173182179 Reorder the terms: 2.2 + x = -11.173182179 Solving 2.2 + x = -11.173182179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -11.173182179 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -11.173182179 + -2.2 x = -11.173182179 + -2.2 Combine like terms: -11.173182179 + -2.2 = -13.373182179 x = -13.373182179 Simplifying x = -13.373182179Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.973182179, -13.373182179}
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