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Simplifying (2x + -4)(x + 6) = 148 Reorder the terms: (-4 + 2x)(x + 6) = 148 Reorder the terms: (-4 + 2x)(6 + x) = 148 Multiply (-4 + 2x) * (6 + x) (-4(6 + x) + 2x * (6 + x)) = 148 ((6 * -4 + x * -4) + 2x * (6 + x)) = 148 ((-24 + -4x) + 2x * (6 + x)) = 148 (-24 + -4x + (6 * 2x + x * 2x)) = 148 (-24 + -4x + (12x + 2x2)) = 148 Combine like terms: -4x + 12x = 8x (-24 + 8x + 2x2) = 148 Solving -24 + 8x + 2x2 = 148 Solving for variable 'x'. Reorder the terms: -24 + -148 + 8x + 2x2 = 148 + -148 Combine like terms: -24 + -148 = -172 -172 + 8x + 2x2 = 148 + -148 Combine like terms: 148 + -148 = 0 -172 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-86 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-86 + 4x + x2)' equal to zero and attempt to solve: Simplifying -86 + 4x + x2 = 0 Solving -86 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + 4x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + 4x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + 4x + x2 = 0 + 86 4x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 4x + x2 = 86 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 = 86 + 4 Reorder the terms: 4 + 4x + x2 = 86 + 4 Combine like terms: 86 + 4 = 90 4 + 4x + x2 = 90 Factor a perfect square on the left side: (x + 2)(x + 2) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 2) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 2 = 9.486832981 Simplifying x + 2 = 9.486832981 Reorder the terms: 2 + x = 9.486832981 Solving 2 + x = 9.486832981 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 = 9.486832981 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.486832981 + -2 x = 9.486832981 + -2 Combine like terms: 9.486832981 + -2 = 7.486832981 x = 7.486832981 Simplifying x = 7.486832981Subproblem 2
x + 2 = -9.486832981 Simplifying x + 2 = -9.486832981 Reorder the terms: 2 + x = -9.486832981 Solving 2 + x = -9.486832981 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 = -9.486832981 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.486832981 + -2 x = -9.486832981 + -2 Combine like terms: -9.486832981 + -2 = -11.486832981 x = -11.486832981 Simplifying x = -11.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.486832981, -11.486832981}Solution
x = {7.486832981, -11.486832981}
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