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Simplifying x2 + 14.6x + -64 = 0 Reorder the terms: -64 + 14.6x + x2 = 0 Solving -64 + 14.6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 14.6x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 14.6x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 14.6x + x2 = 0 + 64 14.6x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 14.6x + x2 = 64 The x term is 14.6x. Take half its coefficient (7.3). Square it (53.29) and add it to both sides. Add '53.29' to each side of the equation. 14.6x + 53.29 + x2 = 64 + 53.29 Reorder the terms: 53.29 + 14.6x + x2 = 64 + 53.29 Combine like terms: 64 + 53.29 = 117.29 53.29 + 14.6x + x2 = 117.29 Factor a perfect square on the left side: (x + 7.3)(x + 7.3) = 117.29 Calculate the square root of the right side: 10.830050785 Break this problem into two subproblems by setting (x + 7.3) equal to 10.830050785 and -10.830050785.Subproblem 1
x + 7.3 = 10.830050785 Simplifying x + 7.3 = 10.830050785 Reorder the terms: 7.3 + x = 10.830050785 Solving 7.3 + x = 10.830050785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + x = 10.830050785 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + x = 10.830050785 + -7.3 x = 10.830050785 + -7.3 Combine like terms: 10.830050785 + -7.3 = 3.530050785 x = 3.530050785 Simplifying x = 3.530050785Subproblem 2
x + 7.3 = -10.830050785 Simplifying x + 7.3 = -10.830050785 Reorder the terms: 7.3 + x = -10.830050785 Solving 7.3 + x = -10.830050785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + x = -10.830050785 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + x = -10.830050785 + -7.3 x = -10.830050785 + -7.3 Combine like terms: -10.830050785 + -7.3 = -18.130050785 x = -18.130050785 Simplifying x = -18.130050785Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.530050785, -18.130050785}
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