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Simplifying x2 = 7 + -6.4x Solving x2 = 7 + -6.4x Solving for variable 'x'. Reorder the terms: -7 + 6.4x + x2 = 7 + -6.4x + -7 + 6.4x Reorder the terms: -7 + 6.4x + x2 = 7 + -7 + -6.4x + 6.4x Combine like terms: 7 + -7 = 0 -7 + 6.4x + x2 = 0 + -6.4x + 6.4x -7 + 6.4x + x2 = -6.4x + 6.4x Combine like terms: -6.4x + 6.4x = 0.0 -7 + 6.4x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 6.4x + 7 + x2 = 0.0 + 7 Reorder the terms: -7 + 7 + 6.4x + x2 = 0.0 + 7 Combine like terms: -7 + 7 = 0 0 + 6.4x + x2 = 0.0 + 7 6.4x + x2 = 0.0 + 7 Combine like terms: 0.0 + 7 = 7 6.4x + x2 = 7 The x term is 6.4x. Take half its coefficient (3.2). Square it (10.24) and add it to both sides. Add '10.24' to each side of the equation. 6.4x + 10.24 + x2 = 7 + 10.24 Reorder the terms: 10.24 + 6.4x + x2 = 7 + 10.24 Combine like terms: 7 + 10.24 = 17.24 10.24 + 6.4x + x2 = 17.24 Factor a perfect square on the left side: (x + 3.2)(x + 3.2) = 17.24 Calculate the square root of the right side: 4.152107898 Break this problem into two subproblems by setting (x + 3.2) equal to 4.152107898 and -4.152107898.Subproblem 1
x + 3.2 = 4.152107898 Simplifying x + 3.2 = 4.152107898 Reorder the terms: 3.2 + x = 4.152107898 Solving 3.2 + x = 4.152107898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = 4.152107898 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = 4.152107898 + -3.2 x = 4.152107898 + -3.2 Combine like terms: 4.152107898 + -3.2 = 0.952107898 x = 0.952107898 Simplifying x = 0.952107898Subproblem 2
x + 3.2 = -4.152107898 Simplifying x + 3.2 = -4.152107898 Reorder the terms: 3.2 + x = -4.152107898 Solving 3.2 + x = -4.152107898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.2' to each side of the equation. 3.2 + -3.2 + x = -4.152107898 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + x = -4.152107898 + -3.2 x = -4.152107898 + -3.2 Combine like terms: -4.152107898 + -3.2 = -7.352107898 x = -7.352107898 Simplifying x = -7.352107898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.952107898, -7.352107898}
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