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Simplifying x2 + 81x + -63 = 0 Reorder the terms: -63 + 81x + x2 = 0 Solving -63 + 81x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 81x + 63 + x2 = 0 + 63 Reorder the terms: -63 + 63 + 81x + x2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 81x + x2 = 0 + 63 81x + x2 = 0 + 63 Combine like terms: 0 + 63 = 63 81x + x2 = 63 The x term is 81x. Take half its coefficient (40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. 81x + 1640.25 + x2 = 63 + 1640.25 Reorder the terms: 1640.25 + 81x + x2 = 63 + 1640.25 Combine like terms: 63 + 1640.25 = 1703.25 1640.25 + 81x + x2 = 1703.25 Factor a perfect square on the left side: (x + 40.5)(x + 40.5) = 1703.25 Calculate the square root of the right side: 41.270449477 Break this problem into two subproblems by setting (x + 40.5) equal to 41.270449477 and -41.270449477.Subproblem 1
x + 40.5 = 41.270449477 Simplifying x + 40.5 = 41.270449477 Reorder the terms: 40.5 + x = 41.270449477 Solving 40.5 + x = 41.270449477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = 41.270449477 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = 41.270449477 + -40.5 x = 41.270449477 + -40.5 Combine like terms: 41.270449477 + -40.5 = 0.770449477 x = 0.770449477 Simplifying x = 0.770449477Subproblem 2
x + 40.5 = -41.270449477 Simplifying x + 40.5 = -41.270449477 Reorder the terms: 40.5 + x = -41.270449477 Solving 40.5 + x = -41.270449477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40.5' to each side of the equation. 40.5 + -40.5 + x = -41.270449477 + -40.5 Combine like terms: 40.5 + -40.5 = 0.0 0.0 + x = -41.270449477 + -40.5 x = -41.270449477 + -40.5 Combine like terms: -41.270449477 + -40.5 = -81.770449477 x = -81.770449477 Simplifying x = -81.770449477Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.770449477, -81.770449477}
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