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Simplifying 14x + -1x2 = -61 Solving 14x + -1x2 = -61 Solving for variable 'x'. Reorder the terms: 61 + 14x + -1x2 = -61 + 61 Combine like terms: -61 + 61 = 0 61 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -61 + -14x + x2 = 0 Move the constant term to the right: Add '61' to each side of the equation. -61 + -14x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + -14x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + -14x + x2 = 0 + 61 -14x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 -14x + x2 = 61 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 = 61 + 49 Reorder the terms: 49 + -14x + x2 = 61 + 49 Combine like terms: 61 + 49 = 110 49 + -14x + x2 = 110 Factor a perfect square on the left side: (x + -7)(x + -7) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + -7) equal to 10.488088482 and -10.488088482.Subproblem 1
x + -7 = 10.488088482 Simplifying x + -7 = 10.488088482 Reorder the terms: -7 + x = 10.488088482 Solving -7 + x = 10.488088482 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 = 10.488088482 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.488088482 + 7 x = 10.488088482 + 7 Combine like terms: 10.488088482 + 7 = 17.488088482 x = 17.488088482 Simplifying x = 17.488088482Subproblem 2
x + -7 = -10.488088482 Simplifying x + -7 = -10.488088482 Reorder the terms: -7 + x = -10.488088482 Solving -7 + x = -10.488088482 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 = -10.488088482 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.488088482 + 7 x = -10.488088482 + 7 Combine like terms: -10.488088482 + 7 = -3.488088482 x = -3.488088482 Simplifying x = -3.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.488088482, -3.488088482}
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