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Simplifying -1(x2 + 14x + 32) = 0 Reorder the terms: -1(32 + 14x + x2) = 0 (32 * -1 + 14x * -1 + x2 * -1) = 0 (-32 + -14x + -1x2) = 0 Solving -32 + -14x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(32 + 14x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(32 + 14x + x2)' equal to zero and attempt to solve: Simplifying 32 + 14x + x2 = 0 Solving 32 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + 14x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + 14x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 14x + x2 = 0 + -32 14x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 14x + x2 = -32 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 = -32 + 49 Reorder the terms: 49 + 14x + x2 = -32 + 49 Combine like terms: -32 + 49 = 17 49 + 14x + x2 = 17 Factor a perfect square on the left side: (x + 7)(x + 7) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + 7) equal to 4.123105626 and -4.123105626.Subproblem 1
x + 7 = 4.123105626 Simplifying x + 7 = 4.123105626 Reorder the terms: 7 + x = 4.123105626 Solving 7 + x = 4.123105626 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 = 4.123105626 + -7 Combine like terms: 7 + -7 = 0 0 + x = 4.123105626 + -7 x = 4.123105626 + -7 Combine like terms: 4.123105626 + -7 = -2.876894374 x = -2.876894374 Simplifying x = -2.876894374Subproblem 2
x + 7 = -4.123105626 Simplifying x + 7 = -4.123105626 Reorder the terms: 7 + x = -4.123105626 Solving 7 + x = -4.123105626 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 = -4.123105626 + -7 Combine like terms: 7 + -7 = 0 0 + x = -4.123105626 + -7 x = -4.123105626 + -7 Combine like terms: -4.123105626 + -7 = -11.123105626 x = -11.123105626 Simplifying x = -11.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.876894374, -11.123105626}Solution
x = {-2.876894374, -11.123105626}
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