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Simplifying -1x2 + 14x + 75 = 0 Reorder the terms: 75 + 14x + -1x2 = 0 Solving 75 + 14x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -75 + -14x + x2 = 0 Move the constant term to the right: Add '75' to each side of the equation. -75 + -14x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + -14x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + -14x + x2 = 0 + 75 -14x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 -14x + x2 = 75 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 = 75 + 49 Reorder the terms: 49 + -14x + x2 = 75 + 49 Combine like terms: 75 + 49 = 124 49 + -14x + x2 = 124 Factor a perfect square on the left side: (x + -7)(x + -7) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (x + -7) equal to 11.135528726 and -11.135528726.Subproblem 1
x + -7 = 11.135528726 Simplifying x + -7 = 11.135528726 Reorder the terms: -7 + x = 11.135528726 Solving -7 + x = 11.135528726 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 = 11.135528726 + 7 Combine like terms: -7 + 7 = 0 0 + x = 11.135528726 + 7 x = 11.135528726 + 7 Combine like terms: 11.135528726 + 7 = 18.135528726 x = 18.135528726 Simplifying x = 18.135528726Subproblem 2
x + -7 = -11.135528726 Simplifying x + -7 = -11.135528726 Reorder the terms: -7 + x = -11.135528726 Solving -7 + x = -11.135528726 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 = -11.135528726 + 7 Combine like terms: -7 + 7 = 0 0 + x = -11.135528726 + 7 x = -11.135528726 + 7 Combine like terms: -11.135528726 + 7 = -4.135528726 x = -4.135528726 Simplifying x = -4.135528726Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.135528726, -4.135528726}
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