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Simplifying -1(x2 + 14x + 21) = 0 Reorder the terms: -1(21 + 14x + x2) = 0 (21 * -1 + 14x * -1 + x2 * -1) = 0 (-21 + -14x + -1x2) = 0 Solving -21 + -14x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(21 + 14x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(21 + 14x + x2)' equal to zero and attempt to solve: Simplifying 21 + 14x + x2 = 0 Solving 21 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 14x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 14x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 14x + x2 = 0 + -21 14x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 14x + x2 = -21 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 = -21 + 49 Reorder the terms: 49 + 14x + x2 = -21 + 49 Combine like terms: -21 + 49 = 28 49 + 14x + x2 = 28 Factor a perfect square on the left side: (x + 7)(x + 7) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (x + 7) equal to 5.291502622 and -5.291502622.Subproblem 1
x + 7 = 5.291502622 Simplifying x + 7 = 5.291502622 Reorder the terms: 7 + x = 5.291502622 Solving 7 + x = 5.291502622 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 = 5.291502622 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.291502622 + -7 x = 5.291502622 + -7 Combine like terms: 5.291502622 + -7 = -1.708497378 x = -1.708497378 Simplifying x = -1.708497378Subproblem 2
x + 7 = -5.291502622 Simplifying x + 7 = -5.291502622 Reorder the terms: 7 + x = -5.291502622 Solving 7 + x = -5.291502622 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 = -5.291502622 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.291502622 + -7 x = -5.291502622 + -7 Combine like terms: -5.291502622 + -7 = -12.291502622 x = -12.291502622 Simplifying x = -12.291502622Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.708497378, -12.291502622}Solution
x = {-1.708497378, -12.291502622}
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