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Simplifying x2 = 23(x + 11) Reorder the terms: x2 = 23(11 + x) x2 = (11 * 23 + x * 23) x2 = (253 + 23x) Solving x2 = 253 + 23x Solving for variable 'x'. Reorder the terms: -253 + -23x + x2 = 253 + 23x + -253 + -23x Reorder the terms: -253 + -23x + x2 = 253 + -253 + 23x + -23x Combine like terms: 253 + -253 = 0 -253 + -23x + x2 = 0 + 23x + -23x -253 + -23x + x2 = 23x + -23x Combine like terms: 23x + -23x = 0 -253 + -23x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '253' to each side of the equation. -253 + -23x + 253 + x2 = 0 + 253 Reorder the terms: -253 + 253 + -23x + x2 = 0 + 253 Combine like terms: -253 + 253 = 0 0 + -23x + x2 = 0 + 253 -23x + x2 = 0 + 253 Combine like terms: 0 + 253 = 253 -23x + x2 = 253 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 = 253 + 132.25 Reorder the terms: 132.25 + -23x + x2 = 253 + 132.25 Combine like terms: 253 + 132.25 = 385.25 132.25 + -23x + x2 = 385.25 Factor a perfect square on the left side: (x + -11.5)(x + -11.5) = 385.25 Calculate the square root of the right side: 19.627786426 Break this problem into two subproblems by setting (x + -11.5) equal to 19.627786426 and -19.627786426.Subproblem 1
x + -11.5 = 19.627786426 Simplifying x + -11.5 = 19.627786426 Reorder the terms: -11.5 + x = 19.627786426 Solving -11.5 + x = 19.627786426 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 = 19.627786426 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 19.627786426 + 11.5 x = 19.627786426 + 11.5 Combine like terms: 19.627786426 + 11.5 = 31.127786426 x = 31.127786426 Simplifying x = 31.127786426Subproblem 2
x + -11.5 = -19.627786426 Simplifying x + -11.5 = -19.627786426 Reorder the terms: -11.5 + x = -19.627786426 Solving -11.5 + x = -19.627786426 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 = -19.627786426 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -19.627786426 + 11.5 x = -19.627786426 + 11.5 Combine like terms: -19.627786426 + 11.5 = -8.127786426 x = -8.127786426 Simplifying x = -8.127786426Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.127786426, -8.127786426}
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