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Simplifying x2 = 9x + -7 Reorder the terms: x2 = -7 + 9x Solving x2 = -7 + 9x Solving for variable 'x'. Reorder the terms: 7 + -9x + x2 = -7 + 9x + 7 + -9x Reorder the terms: 7 + -9x + x2 = -7 + 7 + 9x + -9x Combine like terms: -7 + 7 = 0 7 + -9x + x2 = 0 + 9x + -9x 7 + -9x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 7 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -9x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -9x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9x + x2 = 0 + -7 -9x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -9x + x2 = -7 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 = -7 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -7 + 20.25 Combine like terms: -7 + 20.25 = 13.25 20.25 + -9x + x2 = 13.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + -4.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + -4.5 = 3.640054945 Simplifying x + -4.5 = 3.640054945 Reorder the terms: -4.5 + x = 3.640054945 Solving -4.5 + x = 3.640054945 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 = 3.640054945 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.640054945 + 4.5 x = 3.640054945 + 4.5 Combine like terms: 3.640054945 + 4.5 = 8.140054945 x = 8.140054945 Simplifying x = 8.140054945Subproblem 2
x + -4.5 = -3.640054945 Simplifying x + -4.5 = -3.640054945 Reorder the terms: -4.5 + x = -3.640054945 Solving -4.5 + x = -3.640054945 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 = -3.640054945 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.640054945 + 4.5 x = -3.640054945 + 4.5 Combine like terms: -3.640054945 + 4.5 = 0.859945055 x = 0.859945055 Simplifying x = 0.859945055Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.140054945, 0.859945055}
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