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Simplifying x2 + 6.9x = 128 Reorder the terms: 6.9x + x2 = 128 Solving 6.9x + x2 = 128 Solving for variable 'x'. Reorder the terms: -128 + 6.9x + x2 = 128 + -128 Combine like terms: 128 + -128 = 0 -128 + 6.9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '128' to each side of the equation. -128 + 6.9x + 128 + x2 = 0 + 128 Reorder the terms: -128 + 128 + 6.9x + x2 = 0 + 128 Combine like terms: -128 + 128 = 0 0 + 6.9x + x2 = 0 + 128 6.9x + x2 = 0 + 128 Combine like terms: 0 + 128 = 128 6.9x + x2 = 128 The x term is 6.9x. Take half its coefficient (3.45). Square it (11.9025) and add it to both sides. Add '11.9025' to each side of the equation. 6.9x + 11.9025 + x2 = 128 + 11.9025 Reorder the terms: 11.9025 + 6.9x + x2 = 128 + 11.9025 Combine like terms: 128 + 11.9025 = 139.9025 11.9025 + 6.9x + x2 = 139.9025 Factor a perfect square on the left side: (x + 3.45)(x + 3.45) = 139.9025 Calculate the square root of the right side: 11.828038722 Break this problem into two subproblems by setting (x + 3.45) equal to 11.828038722 and -11.828038722.Subproblem 1
x + 3.45 = 11.828038722 Simplifying x + 3.45 = 11.828038722 Reorder the terms: 3.45 + x = 11.828038722 Solving 3.45 + x = 11.828038722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.45' to each side of the equation. 3.45 + -3.45 + x = 11.828038722 + -3.45 Combine like terms: 3.45 + -3.45 = 0.00 0.00 + x = 11.828038722 + -3.45 x = 11.828038722 + -3.45 Combine like terms: 11.828038722 + -3.45 = 8.378038722 x = 8.378038722 Simplifying x = 8.378038722Subproblem 2
x + 3.45 = -11.828038722 Simplifying x + 3.45 = -11.828038722 Reorder the terms: 3.45 + x = -11.828038722 Solving 3.45 + x = -11.828038722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.45' to each side of the equation. 3.45 + -3.45 + x = -11.828038722 + -3.45 Combine like terms: 3.45 + -3.45 = 0.00 0.00 + x = -11.828038722 + -3.45 x = -11.828038722 + -3.45 Combine like terms: -11.828038722 + -3.45 = -15.278038722 x = -15.278038722 Simplifying x = -15.278038722Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.378038722, -15.278038722}
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