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Simplifying (2x + 4) * x = 140 Reorder the terms: (4 + 2x) * x = 140 Reorder the terms for easier multiplication: x(4 + 2x) = 140 (4 * x + 2x * x) = 140 (4x + 2x2) = 140 Solving 4x + 2x2 = 140 Solving for variable 'x'. Reorder the terms: -140 + 4x + 2x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-70 + 2x + x2) = 0 Ignore the factor 2.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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