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Simplifying 23.5 = x2 + 4x Reorder the terms: 23.5 = 4x + x2 Solving 23.5 = 4x + x2 Solving for variable 'x'. Reorder the terms: 23.5 + -4x + -1x2 = 4x + -4x + x2 + -1x2 Combine like terms: 4x + -4x = 0 23.5 + -4x + -1x2 = 0 + x2 + -1x2 23.5 + -4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 23.5 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -23.5 + 4x + x2 = 0 Move the constant term to the right: Add '23.5' to each side of the equation. -23.5 + 4x + 23.5 + x2 = 0 + 23.5 Reorder the terms: -23.5 + 23.5 + 4x + x2 = 0 + 23.5 Combine like terms: -23.5 + 23.5 = 0.0 0.0 + 4x + x2 = 0 + 23.5 4x + x2 = 0 + 23.5 Combine like terms: 0 + 23.5 = 23.5 4x + x2 = 23.5 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 = 23.5 + 4 Reorder the terms: 4 + 4x + x2 = 23.5 + 4 Combine like terms: 23.5 + 4 = 27.5 4 + 4x + x2 = 27.5 Factor a perfect square on the left side: (x + 2)(x + 2) = 27.5 Calculate the square root of the right side: 5.244044241 Break this problem into two subproblems by setting (x + 2) equal to 5.244044241 and -5.244044241.Subproblem 1
x + 2 = 5.244044241 Simplifying x + 2 = 5.244044241 Reorder the terms: 2 + x = 5.244044241 Solving 2 + x = 5.244044241 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 = 5.244044241 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.244044241 + -2 x = 5.244044241 + -2 Combine like terms: 5.244044241 + -2 = 3.244044241 x = 3.244044241 Simplifying x = 3.244044241Subproblem 2
x + 2 = -5.244044241 Simplifying x + 2 = -5.244044241 Reorder the terms: 2 + x = -5.244044241 Solving 2 + x = -5.244044241 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 = -5.244044241 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.244044241 + -2 x = -5.244044241 + -2 Combine like terms: -5.244044241 + -2 = -7.244044241 x = -7.244044241 Simplifying x = -7.244044241Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.244044241, -7.244044241}
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