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Simplifying 110.25 = x(x + 14) Reorder the terms: 110.25 = x(14 + x) 110.25 = (14 * x + x * x) 110.25 = (14x + x2) Solving 110.25 = 14x + x2 Solving for variable 'x'. Reorder the terms: 110.25 + -14x + -1x2 = 14x + -14x + x2 + -1x2 Combine like terms: 14x + -14x = 0 110.25 + -14x + -1x2 = 0 + x2 + -1x2 110.25 + -14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 110.25 + -14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -110.25 + 14x + x2 = 0 Move the constant term to the right: Add '110.25' to each side of the equation. -110.25 + 14x + 110.25 + x2 = 0 + 110.25 Reorder the terms: -110.25 + 110.25 + 14x + x2 = 0 + 110.25 Combine like terms: -110.25 + 110.25 = 0.00 0.00 + 14x + x2 = 0 + 110.25 14x + x2 = 0 + 110.25 Combine like terms: 0 + 110.25 = 110.25 14x + x2 = 110.25 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 = 110.25 + 49 Reorder the terms: 49 + 14x + x2 = 110.25 + 49 Combine like terms: 110.25 + 49 = 159.25 49 + 14x + x2 = 159.25 Factor a perfect square on the left side: (x + 7)(x + 7) = 159.25 Calculate the square root of the right side: 12.619429464 Break this problem into two subproblems by setting (x + 7) equal to 12.619429464 and -12.619429464.Subproblem 1
x + 7 = 12.619429464 Simplifying x + 7 = 12.619429464 Reorder the terms: 7 + x = 12.619429464 Solving 7 + x = 12.619429464 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 = 12.619429464 + -7 Combine like terms: 7 + -7 = 0 0 + x = 12.619429464 + -7 x = 12.619429464 + -7 Combine like terms: 12.619429464 + -7 = 5.619429464 x = 5.619429464 Simplifying x = 5.619429464Subproblem 2
x + 7 = -12.619429464 Simplifying x + 7 = -12.619429464 Reorder the terms: 7 + x = -12.619429464 Solving 7 + x = -12.619429464 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 = -12.619429464 + -7 Combine like terms: 7 + -7 = 0 0 + x = -12.619429464 + -7 x = -12.619429464 + -7 Combine like terms: -12.619429464 + -7 = -19.619429464 x = -19.619429464 Simplifying x = -19.619429464Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.619429464, -19.619429464}
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