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Simplifying 23.6 = x(x + -3.1) Reorder the terms: 23.6 = x(-3.1 + x) 23.6 = (-3.1 * x + x * x) 23.6 = (-3.1x + x2) Solving 23.6 = -3.1x + x2 Solving for variable 'x'. Reorder the terms: 23.6 + 3.1x + -1x2 = -3.1x + 3.1x + x2 + -1x2 Combine like terms: -3.1x + 3.1x = 0.0 23.6 + 3.1x + -1x2 = 0.0 + x2 + -1x2 23.6 + 3.1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23.6 + 3.1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23.6 + -3.1x + x2 = 0 Move the constant term to the right: Add '23.6' to each side of the equation. -23.6 + -3.1x + 23.6 + x2 = 0 + 23.6 Reorder the terms: -23.6 + 23.6 + -3.1x + x2 = 0 + 23.6 Combine like terms: -23.6 + 23.6 = 0.0 0.0 + -3.1x + x2 = 0 + 23.6 -3.1x + x2 = 0 + 23.6 Combine like terms: 0 + 23.6 = 23.6 -3.1x + x2 = 23.6 The x term is -3.1x. Take half its coefficient (-1.55). Square it (2.4025) and add it to both sides. Add '2.4025' to each side of the equation. -3.1x + 2.4025 + x2 = 23.6 + 2.4025 Reorder the terms: 2.4025 + -3.1x + x2 = 23.6 + 2.4025 Combine like terms: 23.6 + 2.4025 = 26.0025 2.4025 + -3.1x + x2 = 26.0025 Factor a perfect square on the left side: (x + -1.55)(x + -1.55) = 26.0025 Calculate the square root of the right side: 5.099264653 Break this problem into two subproblems by setting (x + -1.55) equal to 5.099264653 and -5.099264653.Subproblem 1
x + -1.55 = 5.099264653 Simplifying x + -1.55 = 5.099264653 Reorder the terms: -1.55 + x = 5.099264653 Solving -1.55 + x = 5.099264653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = 5.099264653 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = 5.099264653 + 1.55 x = 5.099264653 + 1.55 Combine like terms: 5.099264653 + 1.55 = 6.649264653 x = 6.649264653 Simplifying x = 6.649264653Subproblem 2
x + -1.55 = -5.099264653 Simplifying x + -1.55 = -5.099264653 Reorder the terms: -1.55 + x = -5.099264653 Solving -1.55 + x = -5.099264653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.55' to each side of the equation. -1.55 + 1.55 + x = -5.099264653 + 1.55 Combine like terms: -1.55 + 1.55 = 0.00 0.00 + x = -5.099264653 + 1.55 x = -5.099264653 + 1.55 Combine like terms: -5.099264653 + 1.55 = -3.549264653 x = -3.549264653 Simplifying x = -3.549264653Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.649264653, -3.549264653}
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