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Simplifying x2 + -23x = 30 Reorder the terms: -23x + x2 = 30 Solving -23x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -23x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -23x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -23x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -23x + x2 = 0 + 30 -23x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -23x + x2 = 30 The x term is -23x. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x + 132.25 + x2 = 30 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 30 + 132.25 Combine like terms: 30 + 132.25 = 162.25 132.25 + -23x + x2 = 162.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 162.25 Calculate the square root of the right side: 12.737739203 Break this problem into two subproblems by setting (x + -11.5) equal to 12.737739203 and -12.737739203.Subproblem 1
x + -11.5 = 12.737739203 Simplifying x + -11.5 = 12.737739203 Reorder the terms: -11.5 + x = 12.737739203 Solving -11.5 + x = 12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 12.737739203 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 12.737739203 + 11.5 x = 12.737739203 + 11.5 Combine like terms: 12.737739203 + 11.5 = 24.237739203 x = 24.237739203 Simplifying x = 24.237739203Subproblem 2
x + -11.5 = -12.737739203 Simplifying x + -11.5 = -12.737739203 Reorder the terms: -11.5 + x = -12.737739203 Solving -11.5 + x = -12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -12.737739203 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -12.737739203 + 11.5 x = -12.737739203 + 11.5 Combine like terms: -12.737739203 + 11.5 = -1.237739203 x = -1.237739203 Simplifying x = -1.237739203Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.237739203, -1.237739203}
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