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Simplifying x2 + 6.5x + 10 = 0 Reorder the terms: 10 + 6.5x + x2 = 0 Solving 10 + 6.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 6.5x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + 6.5x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 6.5x + x2 = 0 + -10 6.5x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 6.5x + x2 = -10 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 = -10 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = -10 + 10.5625 Combine like terms: -10 + 10.5625 = 0.5625 10.5625 + 6.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + 3.25) equal to 0.75 and -0.75.Subproblem 1
x + 3.25 = 0.75 Simplifying x + 3.25 = 0.75 Reorder the terms: 3.25 + x = 0.75 Solving 3.25 + x = 0.75 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 = 0.75 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 0.75 + -3.25 x = 0.75 + -3.25 Combine like terms: 0.75 + -3.25 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 3.25 = -0.75 Simplifying x + 3.25 = -0.75 Reorder the terms: 3.25 + x = -0.75 Solving 3.25 + x = -0.75 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 = -0.75 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -0.75 + -3.25 x = -0.75 + -3.25 Combine like terms: -0.75 + -3.25 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -4}
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