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Simplifying x * x + 5x = 7 Multiply x * x x2 + 5x = 7 Reorder the terms: 5x + x2 = 7 Solving 5x + x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 5x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 5x + x2 = 0 + 7 5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 5x + x2 = 7 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 7 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 7 + 6.25 Combine like terms: 7 + 6.25 = 13.25 6.25 + 5x + x2 = 13.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x + 2.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x + 2.5 = 3.640054945 Simplifying x + 2.5 = 3.640054945 Reorder the terms: 2.5 + x = 3.640054945 Solving 2.5 + x = 3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.640054945 + -2.5 x = 3.640054945 + -2.5 Combine like terms: 3.640054945 + -2.5 = 1.140054945 x = 1.140054945 Simplifying x = 1.140054945Subproblem 2
x + 2.5 = -3.640054945 Simplifying x + 2.5 = -3.640054945 Reorder the terms: 2.5 + x = -3.640054945 Solving 2.5 + x = -3.640054945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.640054945 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.640054945 + -2.5 x = -3.640054945 + -2.5 Combine like terms: -3.640054945 + -2.5 = -6.140054945 x = -6.140054945 Simplifying x = -6.140054945Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.140054945, -6.140054945}
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