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Simplifying x2 + 9x + -1326 = 0 Reorder the terms: -1326 + 9x + x2 = 0 Solving -1326 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1326' to each side of the equation. -1326 + 9x + 1326 + x2 = 0 + 1326 Reorder the terms: -1326 + 1326 + 9x + x2 = 0 + 1326 Combine like terms: -1326 + 1326 = 0 0 + 9x + x2 = 0 + 1326 9x + x2 = 0 + 1326 Combine like terms: 0 + 1326 = 1326 9x + x2 = 1326 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 1326 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 1326 + 20.25 Combine like terms: 1326 + 20.25 = 1346.25 20.25 + 9x + x2 = 1346.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 1346.25 Calculate the square root of the right side: 36.691279618 Break this problem into two subproblems by setting (x + 4.5) equal to 36.691279618 and -36.691279618.Subproblem 1
x + 4.5 = 36.691279618 Simplifying x + 4.5 = 36.691279618 Reorder the terms: 4.5 + x = 36.691279618 Solving 4.5 + x = 36.691279618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 36.691279618 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 36.691279618 + -4.5 x = 36.691279618 + -4.5 Combine like terms: 36.691279618 + -4.5 = 32.191279618 x = 32.191279618 Simplifying x = 32.191279618Subproblem 2
x + 4.5 = -36.691279618 Simplifying x + 4.5 = -36.691279618 Reorder the terms: 4.5 + x = -36.691279618 Solving 4.5 + x = -36.691279618 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -36.691279618 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -36.691279618 + -4.5 x = -36.691279618 + -4.5 Combine like terms: -36.691279618 + -4.5 = -41.191279618 x = -41.191279618 Simplifying x = -41.191279618Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.191279618, -41.191279618}
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