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Simplifying 5.6x + 3 = x2 Reorder the terms: 3 + 5.6x = x2 Solving 3 + 5.6x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 3 + 5.6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -5.6x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.6x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5.6x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.6x + x2 = 0 + 3 -5.6x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.6x + x2 = 3 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 3 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 3 + 7.84 Combine like terms: 3 + 7.84 = 10.84 7.84 + -5.6x + x2 = 10.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 10.84 Calculate the square root of the right side: 3.292415527 Break this problem into two subproblems by setting (x + -2.8) equal to 3.292415527 and -3.292415527.Subproblem 1
x + -2.8 = 3.292415527 Simplifying x + -2.8 = 3.292415527 Reorder the terms: -2.8 + x = 3.292415527 Solving -2.8 + x = 3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 3.292415527 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 3.292415527 + 2.8 x = 3.292415527 + 2.8 Combine like terms: 3.292415527 + 2.8 = 6.092415527 x = 6.092415527 Simplifying x = 6.092415527Subproblem 2
x + -2.8 = -3.292415527 Simplifying x + -2.8 = -3.292415527 Reorder the terms: -2.8 + x = -3.292415527 Solving -2.8 + x = -3.292415527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -3.292415527 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -3.292415527 + 2.8 x = -3.292415527 + 2.8 Combine like terms: -3.292415527 + 2.8 = -0.492415527 x = -0.492415527 Simplifying x = -0.492415527Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.092415527, -0.492415527}
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