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Simplifying x2 + -9x + -92 = 7 Reorder the terms: -92 + -9x + x2 = 7 Solving -92 + -9x + x2 = 7 Solving for variable 'x'. Reorder the terms: -92 + -7 + -9x + x2 = 7 + -7 Combine like terms: -92 + -7 = -99 -99 + -9x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -99 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + -9x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + -9x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + -9x + x2 = 0 + 99 -9x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 -9x + x2 = 99 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 99 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 99 + 20.25 Combine like terms: 99 + 20.25 = 119.25 20.25 + -9x + x2 = 119.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 119.25 Calculate the square root of the right side: 10.920164834 Break this problem into two subproblems by setting (x + -4.5) equal to 10.920164834 and -10.920164834.Subproblem 1
x + -4.5 = 10.920164834 Simplifying x + -4.5 = 10.920164834 Reorder the terms: -4.5 + x = 10.920164834 Solving -4.5 + x = 10.920164834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 10.920164834 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 10.920164834 + 4.5 x = 10.920164834 + 4.5 Combine like terms: 10.920164834 + 4.5 = 15.420164834 x = 15.420164834 Simplifying x = 15.420164834Subproblem 2
x + -4.5 = -10.920164834 Simplifying x + -4.5 = -10.920164834 Reorder the terms: -4.5 + x = -10.920164834 Solving -4.5 + x = -10.920164834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -10.920164834 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -10.920164834 + 4.5 x = -10.920164834 + 4.5 Combine like terms: -10.920164834 + 4.5 = -6.420164834 x = -6.420164834 Simplifying x = -6.420164834Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.420164834, -6.420164834}
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