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Simplifying x2 = 23x + -63 Reorder the terms: x2 = -63 + 23x Solving x2 = -63 + 23x Solving for variable 'x'. Reorder the terms: 63 + -23x + x2 = -63 + 23x + 63 + -23x Reorder the terms: 63 + -23x + x2 = -63 + 63 + 23x + -23x Combine like terms: -63 + 63 = 0 63 + -23x + x2 = 0 + 23x + -23x 63 + -23x + x2 = 23x + -23x Combine like terms: 23x + -23x = 0 63 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -23x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + -23x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -23x + x2 = 0 + -63 -23x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 -23x + x2 = -63 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 = -63 + 132.25 Reorder the terms: 132.25 + -23x + x2 = -63 + 132.25 Combine like terms: -63 + 132.25 = 69.25 132.25 + -23x + x2 = 69.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 69.25 Calculate the square root of the right side: 8.321658489 Break this problem into two subproblems by setting (x + -11.5) equal to 8.321658489 and -8.321658489.Subproblem 1
x + -11.5 = 8.321658489 Simplifying x + -11.5 = 8.321658489 Reorder the terms: -11.5 + x = 8.321658489 Solving -11.5 + x = 8.321658489 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 = 8.321658489 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 8.321658489 + 11.5 x = 8.321658489 + 11.5 Combine like terms: 8.321658489 + 11.5 = 19.821658489 x = 19.821658489 Simplifying x = 19.821658489Subproblem 2
x + -11.5 = -8.321658489 Simplifying x + -11.5 = -8.321658489 Reorder the terms: -11.5 + x = -8.321658489 Solving -11.5 + x = -8.321658489 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 = -8.321658489 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -8.321658489 + 11.5 x = -8.321658489 + 11.5 Combine like terms: -8.321658489 + 11.5 = 3.178341511 x = 3.178341511 Simplifying x = 3.178341511Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.821658489, 3.178341511}
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