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Simplifying x2 + 14.5x + 7 = 0 Reorder the terms: 7 + 14.5x + x2 = 0 Solving 7 + 14.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 14.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 14.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 14.5x + x2 = 0 + -7 14.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 14.5x + x2 = -7 The x term is 14.5x. Take half its coefficient (7.25). Square it (52.5625) and add it to both sides. Add '52.5625' to each side of the equation. 14.5x + 52.5625 + x2 = -7 + 52.5625 Reorder the terms: 52.5625 + 14.5x + x2 = -7 + 52.5625 Combine like terms: -7 + 52.5625 = 45.5625 52.5625 + 14.5x + x2 = 45.5625 Factor a perfect square on the left side: (x + 7.25)(x + 7.25) = 45.5625 Calculate the square root of the right side: 6.75 Break this problem into two subproblems by setting (x + 7.25) equal to 6.75 and -6.75.Subproblem 1
x + 7.25 = 6.75 Simplifying x + 7.25 = 6.75 Reorder the terms: 7.25 + x = 6.75 Solving 7.25 + x = 6.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = 6.75 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = 6.75 + -7.25 x = 6.75 + -7.25 Combine like terms: 6.75 + -7.25 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 7.25 = -6.75 Simplifying x + 7.25 = -6.75 Reorder the terms: 7.25 + x = -6.75 Solving 7.25 + x = -6.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.25' to each side of the equation. 7.25 + -7.25 + x = -6.75 + -7.25 Combine like terms: 7.25 + -7.25 = 0.00 0.00 + x = -6.75 + -7.25 x = -6.75 + -7.25 Combine like terms: -6.75 + -7.25 = -14 x = -14 Simplifying x = -14Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -14}
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