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Simplifying x2 + -6.5x = 42 Reorder the terms: -6.5x + x2 = 42 Solving -6.5x + x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + -6.5x + x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + -6.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -6.5x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -6.5x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -6.5x + x2 = 0 + 42 -6.5x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -6.5x + x2 = 42 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 42 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 42 + 10.5625 Combine like terms: 42 + 10.5625 = 52.5625 10.5625 + -6.5x + x2 = 52.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 52.5625 Calculate the square root of the right side: 7.25 Break this problem into two subproblems by setting (x + -3.25) equal to 7.25 and -7.25.Subproblem 1
x + -3.25 = 7.25 Simplifying x + -3.25 = 7.25 Reorder the terms: -3.25 + x = 7.25 Solving -3.25 + x = 7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 7.25 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 7.25 + 3.25 x = 7.25 + 3.25 Combine like terms: 7.25 + 3.25 = 10.5 x = 10.5 Simplifying x = 10.5Subproblem 2
x + -3.25 = -7.25 Simplifying x + -3.25 = -7.25 Reorder the terms: -3.25 + x = -7.25 Solving -3.25 + x = -7.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -7.25 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -7.25 + 3.25 x = -7.25 + 3.25 Combine like terms: -7.25 + 3.25 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.5, -4}
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