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Simplifying x2 + -24x + -7 = 0 Reorder the terms: -7 + -24x + x2 = 0 Solving -7 + -24x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -24x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -24x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -24x + x2 = 0 + 7 -24x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -24x + x2 = 7 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 7 + 144 Reorder the terms: 144 + -24x + x2 = 7 + 144 Combine like terms: 7 + 144 = 151 144 + -24x + x2 = 151 Factor a perfect square on the left side: (x + -12)(x + -12) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + -12) equal to 12.288205727 and -12.288205727.Subproblem 1
x + -12 = 12.288205727 Simplifying x + -12 = 12.288205727 Reorder the terms: -12 + x = 12.288205727 Solving -12 + x = 12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.288205727 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.288205727 + 12 x = 12.288205727 + 12 Combine like terms: 12.288205727 + 12 = 24.288205727 x = 24.288205727 Simplifying x = 24.288205727Subproblem 2
x + -12 = -12.288205727 Simplifying x + -12 = -12.288205727 Reorder the terms: -12 + x = -12.288205727 Solving -12 + x = -12.288205727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.288205727 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.288205727 + 12 x = -12.288205727 + 12 Combine like terms: -12.288205727 + 12 = -0.288205727 x = -0.288205727 Simplifying x = -0.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.288205727, -0.288205727}
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