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Simplifying 48 = x2 + -14x Reorder the terms: 48 = -14x + x2 Solving 48 = -14x + x2 Solving for variable 'x'. Reorder the terms: 48 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 48 + 14x + -1x2 = 0 + x2 + -1x2 48 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 48 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -48 + -14x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -14x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -14x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -14x + x2 = 0 + 48 -14x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -14x + x2 = 48 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 = 48 + 49 Reorder the terms: 49 + -14x + x2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + -14x + x2 = 97 Factor a perfect square on the left side: (x + -7)(x + -7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + -7) equal to 9.848857802 and -9.848857802.Subproblem 1
x + -7 = 9.848857802 Simplifying x + -7 = 9.848857802 Reorder the terms: -7 + x = 9.848857802 Solving -7 + x = 9.848857802 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 = 9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.848857802 + 7 x = 9.848857802 + 7 Combine like terms: 9.848857802 + 7 = 16.848857802 x = 16.848857802 Simplifying x = 16.848857802Subproblem 2
x + -7 = -9.848857802 Simplifying x + -7 = -9.848857802 Reorder the terms: -7 + x = -9.848857802 Solving -7 + x = -9.848857802 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 = -9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.848857802 + 7 x = -9.848857802 + 7 Combine like terms: -9.848857802 + 7 = -2.848857802 x = -2.848857802 Simplifying x = -2.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.848857802, -2.848857802}
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