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Simplifying x2 + -9x + 2x + 21 = 80 Reorder the terms: 21 + -9x + 2x + x2 = 80 Combine like terms: -9x + 2x = -7x 21 + -7x + x2 = 80 Solving 21 + -7x + x2 = 80 Solving for variable 'x'. Reorder the terms: 21 + -80 + -7x + x2 = 80 + -80 Combine like terms: 21 + -80 = -59 -59 + -7x + x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -59 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -7x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + -7x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -7x + x2 = 0 + 59 -7x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 -7x + x2 = 59 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 59 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 59 + 12.25 Combine like terms: 59 + 12.25 = 71.25 12.25 + -7x + x2 = 71.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + -3.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + -3.5 = 8.440971508 Simplifying x + -3.5 = 8.440971508 Reorder the terms: -3.5 + x = 8.440971508 Solving -3.5 + x = 8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 8.440971508 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 8.440971508 + 3.5 x = 8.440971508 + 3.5 Combine like terms: 8.440971508 + 3.5 = 11.940971508 x = 11.940971508 Simplifying x = 11.940971508Subproblem 2
x + -3.5 = -8.440971508 Simplifying x + -3.5 = -8.440971508 Reorder the terms: -3.5 + x = -8.440971508 Solving -3.5 + x = -8.440971508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -8.440971508 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -8.440971508 + 3.5 x = -8.440971508 + 3.5 Combine like terms: -8.440971508 + 3.5 = -4.940971508 x = -4.940971508 Simplifying x = -4.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.940971508, -4.940971508}
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