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Simplifying 3x2 = 3 + -42x Solving 3x2 = 3 + -42x Solving for variable 'x'. Reorder the terms: -3 + 42x + 3x2 = 3 + -42x + -3 + 42x Reorder the terms: -3 + 42x + 3x2 = 3 + -3 + -42x + 42x Combine like terms: 3 + -3 = 0 -3 + 42x + 3x2 = 0 + -42x + 42x -3 + 42x + 3x2 = -42x + 42x Combine like terms: -42x + 42x = 0 -3 + 42x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + 14x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + 14x + x2)' equal to zero and attempt to solve: Simplifying -1 + 14x + x2 = 0 Solving -1 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 14x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 14x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 14x + x2 = 0 + 1 14x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 14x + x2 = 1 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 = 1 + 49 Reorder the terms: 49 + 14x + x2 = 1 + 49 Combine like terms: 1 + 49 = 50 49 + 14x + x2 = 50 Factor a perfect square on the left side: (x + 7)(x + 7) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (x + 7) equal to 7.071067812 and -7.071067812.Subproblem 1
x + 7 = 7.071067812 Simplifying x + 7 = 7.071067812 Reorder the terms: 7 + x = 7.071067812 Solving 7 + x = 7.071067812 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 = 7.071067812 + -7 Combine like terms: 7 + -7 = 0 0 + x = 7.071067812 + -7 x = 7.071067812 + -7 Combine like terms: 7.071067812 + -7 = 0.071067812 x = 0.071067812 Simplifying x = 0.071067812Subproblem 2
x + 7 = -7.071067812 Simplifying x + 7 = -7.071067812 Reorder the terms: 7 + x = -7.071067812 Solving 7 + x = -7.071067812 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 = -7.071067812 + -7 Combine like terms: 7 + -7 = 0 0 + x = -7.071067812 + -7 x = -7.071067812 + -7 Combine like terms: -7.071067812 + -7 = -14.071067812 x = -14.071067812 Simplifying x = -14.071067812Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.071067812, -14.071067812}Solution
x = {0.071067812, -14.071067812}
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