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Simplifying 2x(x2 + 14x + 42) = 0 Reorder the terms: 2x(42 + 14x + x2) = 0 (42 * 2x + 14x * 2x + x2 * 2x) = 0 (84x + 28x2 + 2x3) = 0 Solving 84x + 28x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(42 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(42 + 14x + x2)' equal to zero and attempt to solve: Simplifying 42 + 14x + x2 = 0 Solving 42 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 14x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 14x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 14x + x2 = 0 + -42 14x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 14x + x2 = -42 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -42 + 49 Reorder the terms: 49 + 14x + x2 = -42 + 49 Combine like terms: -42 + 49 = 7 49 + 14x + x2 = 7 Factor a perfect square on the left side: (x + 7)(x + 7) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 7) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 7 = 2.645751311 Simplifying x + 7 = 2.645751311 Reorder the terms: 7 + x = 2.645751311 Solving 7 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 2.645751311 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.645751311 + -7 x = 2.645751311 + -7 Combine like terms: 2.645751311 + -7 = -4.354248689 x = -4.354248689 Simplifying x = -4.354248689Subproblem 2
x + 7 = -2.645751311 Simplifying x + 7 = -2.645751311 Reorder the terms: 7 + x = -2.645751311 Solving 7 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -2.645751311 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.645751311 + -7 x = -2.645751311 + -7 Combine like terms: -2.645751311 + -7 = -9.645751311 x = -9.645751311 Simplifying x = -9.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.354248689, -9.645751311}Solution
x = {0, -4.354248689, -9.645751311}
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