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Simplifying (x)(x + -4) = 48 Reorder the terms: x(-4 + x) = 48 (-4 * x + x * x) = 48 (-4x + x2) = 48 Solving -4x + x2 = 48 Solving for variable 'x'. Reorder the terms: -48 + -4x + x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -4x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -4x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -4x + x2 = 0 + 48 -4x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -4x + x2 = 48 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 48 + 4 Reorder the terms: 4 + -4x + x2 = 48 + 4 Combine like terms: 48 + 4 = 52 4 + -4x + x2 = 52 Factor a perfect square on the left side: (x + -2)(x + -2) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x + -2) equal to 7.211102551 and -7.211102551.Subproblem 1
x + -2 = 7.211102551 Simplifying x + -2 = 7.211102551 Reorder the terms: -2 + x = 7.211102551 Solving -2 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.211102551 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.211102551 + 2 x = 7.211102551 + 2 Combine like terms: 7.211102551 + 2 = 9.211102551 x = 9.211102551 Simplifying x = 9.211102551Subproblem 2
x + -2 = -7.211102551 Simplifying x + -2 = -7.211102551 Reorder the terms: -2 + x = -7.211102551 Solving -2 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.211102551 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.211102551 + 2 x = -7.211102551 + 2 Combine like terms: -7.211102551 + 2 = -5.211102551 x = -5.211102551 Simplifying x = -5.211102551Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.211102551, -5.211102551}
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