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Simplifying (x + 2)(x)(6) = 420 Reorder the terms: (2 + x)(x)(6) = 420 Reorder the terms for easier multiplication: 6x(2 + x) = 420 (2 * 6x + x * 6x) = 420 (12x + 6x2) = 420 Solving 12x + 6x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 12x + 6x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 12x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-70 + 2x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-70 + 2x + x2)' equal to zero and attempt to solve: Simplifying -70 + 2x + x2 = 0 Solving -70 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '70' to each side of the equation. -70 + 2x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 2x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 2x + x2 = 0 + 70 2x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 2x + x2 = 70 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 = 70 + 1 Reorder the terms: 1 + 2x + x2 = 70 + 1 Combine like terms: 70 + 1 = 71 1 + 2x + x2 = 71 Factor a perfect square on the left side: (x + 1)(x + 1) = 71 Calculate the square root of the right side: 8.426149773 Break this problem into two subproblems by setting (x + 1) equal to 8.426149773 and -8.426149773.Subproblem 1
x + 1 = 8.426149773 Simplifying x + 1 = 8.426149773 Reorder the terms: 1 + x = 8.426149773 Solving 1 + x = 8.426149773 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 = 8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + x = 8.426149773 + -1 x = 8.426149773 + -1 Combine like terms: 8.426149773 + -1 = 7.426149773 x = 7.426149773 Simplifying x = 7.426149773Subproblem 2
x + 1 = -8.426149773 Simplifying x + 1 = -8.426149773 Reorder the terms: 1 + x = -8.426149773 Solving 1 + x = -8.426149773 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 = -8.426149773 + -1 Combine like terms: 1 + -1 = 0 0 + x = -8.426149773 + -1 x = -8.426149773 + -1 Combine like terms: -8.426149773 + -1 = -9.426149773 x = -9.426149773 Simplifying x = -9.426149773Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.426149773, -9.426149773}Solution
x = {7.426149773, -9.426149773}
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