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Simplifying x2 + -14x + 4 = 12 Reorder the terms: 4 + -14x + x2 = 12 Solving 4 + -14x + x2 = 12 Solving for variable 'x'. Reorder the terms: 4 + -12 + -14x + x2 = 12 + -12 Combine like terms: 4 + -12 = -8 -8 + -14x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -8 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -14x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -14x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -14x + x2 = 0 + 8 -14x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -14x + x2 = 8 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 = 8 + 49 Reorder the terms: 49 + -14x + x2 = 8 + 49 Combine like terms: 8 + 49 = 57 49 + -14x + x2 = 57 Factor a perfect square on the left side: (x + -7)(x + -7) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + -7) equal to 7.549834435 and -7.549834435.Subproblem 1
x + -7 = 7.549834435 Simplifying x + -7 = 7.549834435 Reorder the terms: -7 + x = 7.549834435 Solving -7 + x = 7.549834435 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 = 7.549834435 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.549834435 + 7 x = 7.549834435 + 7 Combine like terms: 7.549834435 + 7 = 14.549834435 x = 14.549834435 Simplifying x = 14.549834435Subproblem 2
x + -7 = -7.549834435 Simplifying x + -7 = -7.549834435 Reorder the terms: -7 + x = -7.549834435 Solving -7 + x = -7.549834435 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 = -7.549834435 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.549834435 + 7 x = -7.549834435 + 7 Combine like terms: -7.549834435 + 7 = -0.549834435 x = -0.549834435 Simplifying x = -0.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.549834435, -0.549834435}
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