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Simplifying (2x + 14)(x + -3) = 146 Reorder the terms: (14 + 2x)(x + -3) = 146 Reorder the terms: (14 + 2x)(-3 + x) = 146 Multiply (14 + 2x) * (-3 + x) (14(-3 + x) + 2x * (-3 + x)) = 146 ((-3 * 14 + x * 14) + 2x * (-3 + x)) = 146 ((-42 + 14x) + 2x * (-3 + x)) = 146 (-42 + 14x + (-3 * 2x + x * 2x)) = 146 (-42 + 14x + (-6x + 2x2)) = 146 Combine like terms: 14x + -6x = 8x (-42 + 8x + 2x2) = 146 Solving -42 + 8x + 2x2 = 146 Solving for variable 'x'. Reorder the terms: -42 + -146 + 8x + 2x2 = 146 + -146 Combine like terms: -42 + -146 = -188 -188 + 8x + 2x2 = 146 + -146 Combine like terms: 146 + -146 = 0 -188 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-94 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-94 + 4x + x2)' equal to zero and attempt to solve: Simplifying -94 + 4x + x2 = 0 Solving -94 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '94' to each side of the equation. -94 + 4x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + 4x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 4x + x2 = 0 + 94 4x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 4x + x2 = 94 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 = 94 + 4 Reorder the terms: 4 + 4x + x2 = 94 + 4 Combine like terms: 94 + 4 = 98 4 + 4x + x2 = 98 Factor a perfect square on the left side: (x + 2)(x + 2) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + 2) equal to 9.899494937 and -9.899494937.Subproblem 1
x + 2 = 9.899494937 Simplifying x + 2 = 9.899494937 Reorder the terms: 2 + x = 9.899494937 Solving 2 + x = 9.899494937 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 = 9.899494937 + -2 Combine like terms: 2 + -2 = 0 0 + x = 9.899494937 + -2 x = 9.899494937 + -2 Combine like terms: 9.899494937 + -2 = 7.899494937 x = 7.899494937 Simplifying x = 7.899494937Subproblem 2
x + 2 = -9.899494937 Simplifying x + 2 = -9.899494937 Reorder the terms: 2 + x = -9.899494937 Solving 2 + x = -9.899494937 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 = -9.899494937 + -2 Combine like terms: 2 + -2 = 0 0 + x = -9.899494937 + -2 x = -9.899494937 + -2 Combine like terms: -9.899494937 + -2 = -11.899494937 x = -11.899494937 Simplifying x = -11.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.899494937, -11.899494937}Solution
x = {7.899494937, -11.899494937}
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