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Simplifying 14x + -21 = x2 + 4 Reorder the terms: -21 + 14x = x2 + 4 Reorder the terms: -21 + 14x = 4 + x2 Solving -21 + 14x = 4 + x2 Solving for variable 'x'. Reorder the terms: -21 + -4 + 14x + -1x2 = 4 + x2 + -4 + -1x2 Combine like terms: -21 + -4 = -25 -25 + 14x + -1x2 = 4 + x2 + -4 + -1x2 Reorder the terms: -25 + 14x + -1x2 = 4 + -4 + x2 + -1x2 Combine like terms: 4 + -4 = 0 -25 + 14x + -1x2 = 0 + x2 + -1x2 -25 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -25 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 25 + -14x + x2 = 0 Move the constant term to the right: Add '-25' to each side of the equation. 25 + -14x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -14x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -14x + x2 = 0 + -25 -14x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -14x + x2 = -25 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 = -25 + 49 Reorder the terms: 49 + -14x + x2 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + -14x + x2 = 24 Factor a perfect square on the left side: (x + -7)(x + -7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + -7) equal to 4.898979486 and -4.898979486.Subproblem 1
x + -7 = 4.898979486 Simplifying x + -7 = 4.898979486 Reorder the terms: -7 + x = 4.898979486 Solving -7 + x = 4.898979486 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 = 4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.898979486 + 7 x = 4.898979486 + 7 Combine like terms: 4.898979486 + 7 = 11.898979486 x = 11.898979486 Simplifying x = 11.898979486Subproblem 2
x + -7 = -4.898979486 Simplifying x + -7 = -4.898979486 Reorder the terms: -7 + x = -4.898979486 Solving -7 + x = -4.898979486 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 = -4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.898979486 + 7 x = -4.898979486 + 7 Combine like terms: -4.898979486 + 7 = 2.101020514 x = 2.101020514 Simplifying x = 2.101020514Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.898979486, 2.101020514}
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