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Simplifying (x + 4)(x + -6) = 216 Reorder the terms: (4 + x)(x + -6) = 216 Reorder the terms: (4 + x)(-6 + x) = 216 Multiply (4 + x) * (-6 + x) (4(-6 + x) + x(-6 + x)) = 216 ((-6 * 4 + x * 4) + x(-6 + x)) = 216 ((-24 + 4x) + x(-6 + x)) = 216 (-24 + 4x + (-6 * x + x * x)) = 216 (-24 + 4x + (-6x + x2)) = 216 Combine like terms: 4x + -6x = -2x (-24 + -2x + x2) = 216 Solving -24 + -2x + x2 = 216 Solving for variable 'x'. Reorder the terms: -24 + -216 + -2x + x2 = 216 + -216 Combine like terms: -24 + -216 = -240 -240 + -2x + x2 = 216 + -216 Combine like terms: 216 + -216 = 0 -240 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '240' to each side of the equation. -240 + -2x + 240 + x2 = 0 + 240 Reorder the terms: -240 + 240 + -2x + x2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + -2x + x2 = 0 + 240 -2x + x2 = 0 + 240 Combine like terms: 0 + 240 = 240 -2x + x2 = 240 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 240 + 1 Reorder the terms: 1 + -2x + x2 = 240 + 1 Combine like terms: 240 + 1 = 241 1 + -2x + x2 = 241 Factor a perfect square on the left side: (x + -1)(x + -1) = 241 Calculate the square root of the right side: 15.524174696 Break this problem into two subproblems by setting (x + -1) equal to 15.524174696 and -15.524174696.Subproblem 1
x + -1 = 15.524174696 Simplifying x + -1 = 15.524174696 Reorder the terms: -1 + x = 15.524174696 Solving -1 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 15.524174696 + 1 Combine like terms: -1 + 1 = 0 0 + x = 15.524174696 + 1 x = 15.524174696 + 1 Combine like terms: 15.524174696 + 1 = 16.524174696 x = 16.524174696 Simplifying x = 16.524174696Subproblem 2
x + -1 = -15.524174696 Simplifying x + -1 = -15.524174696 Reorder the terms: -1 + x = -15.524174696 Solving -1 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -15.524174696 + 1 Combine like terms: -1 + 1 = 0 0 + x = -15.524174696 + 1 x = -15.524174696 + 1 Combine like terms: -15.524174696 + 1 = -14.524174696 x = -14.524174696 Simplifying x = -14.524174696Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.524174696, -14.524174696}
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