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Simplifying x2 + -9x = 19 Reorder the terms: -9x + x2 = 19 Solving -9x + x2 = 19 Solving for variable 'x'. Reorder the terms: -19 + -9x + x2 = 19 + -19 Combine like terms: 19 + -19 = 0 -19 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -9x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -9x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -9x + x2 = 0 + 19 -9x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -9x + x2 = 19 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 = 19 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 19 + 20.25 Combine like terms: 19 + 20.25 = 39.25 20.25 + -9x + x2 = 39.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -4.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -4.5 = 6.264982043 Simplifying x + -4.5 = 6.264982043 Reorder the terms: -4.5 + x = 6.264982043 Solving -4.5 + x = 6.264982043 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 = 6.264982043 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.264982043 + 4.5 x = 6.264982043 + 4.5 Combine like terms: 6.264982043 + 4.5 = 10.764982043 x = 10.764982043 Simplifying x = 10.764982043Subproblem 2
x + -4.5 = -6.264982043 Simplifying x + -4.5 = -6.264982043 Reorder the terms: -4.5 + x = -6.264982043 Solving -4.5 + x = -6.264982043 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 = -6.264982043 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.264982043 + 4.5 x = -6.264982043 + 4.5 Combine like terms: -6.264982043 + 4.5 = -1.764982043 x = -1.764982043 Simplifying x = -1.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.764982043, -1.764982043}
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