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Simplifying 2(x2 + 14x + -378) = 0 Reorder the terms: 2(-378 + 14x + x2) = 0 (-378 * 2 + 14x * 2 + x2 * 2) = 0 (-756 + 28x + 2x2) = 0 Solving -756 + 28x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-378 + 14x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-378 + 14x + x2)' equal to zero and attempt to solve: Simplifying -378 + 14x + x2 = 0 Solving -378 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '378' to each side of the equation. -378 + 14x + 378 + x2 = 0 + 378 Reorder the terms: -378 + 378 + 14x + x2 = 0 + 378 Combine like terms: -378 + 378 = 0 0 + 14x + x2 = 0 + 378 14x + x2 = 0 + 378 Combine like terms: 0 + 378 = 378 14x + x2 = 378 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 = 378 + 49 Reorder the terms: 49 + 14x + x2 = 378 + 49 Combine like terms: 378 + 49 = 427 49 + 14x + x2 = 427 Factor a perfect square on the left side: (x + 7)(x + 7) = 427 Calculate the square root of the right side: 20.66397832 Break this problem into two subproblems by setting (x + 7) equal to 20.66397832 and -20.66397832.Subproblem 1
x + 7 = 20.66397832 Simplifying x + 7 = 20.66397832 Reorder the terms: 7 + x = 20.66397832 Solving 7 + x = 20.66397832 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 = 20.66397832 + -7 Combine like terms: 7 + -7 = 0 0 + x = 20.66397832 + -7 x = 20.66397832 + -7 Combine like terms: 20.66397832 + -7 = 13.66397832 x = 13.66397832 Simplifying x = 13.66397832Subproblem 2
x + 7 = -20.66397832 Simplifying x + 7 = -20.66397832 Reorder the terms: 7 + x = -20.66397832 Solving 7 + x = -20.66397832 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 = -20.66397832 + -7 Combine like terms: 7 + -7 = 0 0 + x = -20.66397832 + -7 x = -20.66397832 + -7 Combine like terms: -20.66397832 + -7 = -27.66397832 x = -27.66397832 Simplifying x = -27.66397832Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.66397832, -27.66397832}Solution
x = {13.66397832, -27.66397832}
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