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Simplifying x2 + -88 = 6x Reorder the terms: -88 + x2 = 6x Solving -88 + x2 = 6x Solving for variable 'x'. Reorder the terms: -88 + -6x + x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -88 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -6x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + -6x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -6x + x2 = 0 + 88 -6x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 -6x + x2 = 88 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 88 + 9 Reorder the terms: 9 + -6x + x2 = 88 + 9 Combine like terms: 88 + 9 = 97 9 + -6x + x2 = 97 Factor a perfect square on the left side: (x + -3)(x + -3) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -3) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -3 = 9.848857802 Simplifying x + -3 = 9.848857802 Reorder the terms: -3 + x = 9.848857802 Solving -3 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 9.848857802 + 3 Combine like terms: -3 + 3 = 0 0 + x = 9.848857802 + 3 x = 9.848857802 + 3 Combine like terms: 9.848857802 + 3 = 12.848857802 x = 12.848857802 Simplifying x = 12.848857802Subproblem 2
x + -3 = -9.848857802 Simplifying x + -3 = -9.848857802 Reorder the terms: -3 + x = -9.848857802 Solving -3 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -9.848857802 + 3 Combine like terms: -3 + 3 = 0 0 + x = -9.848857802 + 3 x = -9.848857802 + 3 Combine like terms: -9.848857802 + 3 = -6.848857802 x = -6.848857802 Simplifying x = -6.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.848857802, -6.848857802}
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