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Simplifying x + -7 + 14(x + 7) = (x + -7)(x + 7) Reorder the terms: x + -7 + 14(7 + x) = (x + -7)(x + 7) x + -7 + (7 * 14 + x * 14) = (x + -7)(x + 7) x + -7 + (98 + 14x) = (x + -7)(x + 7) Reorder the terms: -7 + 98 + x + 14x = (x + -7)(x + 7) Combine like terms: -7 + 98 = 91 91 + x + 14x = (x + -7)(x + 7) Combine like terms: x + 14x = 15x 91 + 15x = (x + -7)(x + 7) Reorder the terms: 91 + 15x = (-7 + x)(x + 7) Reorder the terms: 91 + 15x = (-7 + x)(7 + x) Multiply (-7 + x) * (7 + x) 91 + 15x = (-7(7 + x) + x(7 + x)) 91 + 15x = ((7 * -7 + x * -7) + x(7 + x)) 91 + 15x = ((-49 + -7x) + x(7 + x)) 91 + 15x = (-49 + -7x + (7 * x + x * x)) 91 + 15x = (-49 + -7x + (7x + x2)) Combine like terms: -7x + 7x = 0 91 + 15x = (-49 + 0 + x2) 91 + 15x = (-49 + x2) Solving 91 + 15x = -49 + x2 Solving for variable 'x'. Reorder the terms: 91 + 49 + 15x + -1x2 = -49 + x2 + 49 + -1x2 Combine like terms: 91 + 49 = 140 140 + 15x + -1x2 = -49 + x2 + 49 + -1x2 Reorder the terms: 140 + 15x + -1x2 = -49 + 49 + x2 + -1x2 Combine like terms: -49 + 49 = 0 140 + 15x + -1x2 = 0 + x2 + -1x2 140 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 140 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + -15x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -15x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -15x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -15x + x2 = 0 + 140 -15x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -15x + x2 = 140 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 140 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 140 + 56.25 Combine like terms: 140 + 56.25 = 196.25 56.25 + -15x + x2 = 196.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 196.25 Calculate the square root of the right side: 14.008925726 Break this problem into two subproblems by setting (x + -7.5) equal to 14.008925726 and -14.008925726.Subproblem 1
x + -7.5 = 14.008925726 Simplifying x + -7.5 = 14.008925726 Reorder the terms: -7.5 + x = 14.008925726 Solving -7.5 + x = 14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 14.008925726 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 14.008925726 + 7.5 x = 14.008925726 + 7.5 Combine like terms: 14.008925726 + 7.5 = 21.508925726 x = 21.508925726 Simplifying x = 21.508925726Subproblem 2
x + -7.5 = -14.008925726 Simplifying x + -7.5 = -14.008925726 Reorder the terms: -7.5 + x = -14.008925726 Solving -7.5 + x = -14.008925726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -14.008925726 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -14.008925726 + 7.5 x = -14.008925726 + 7.5 Combine like terms: -14.008925726 + 7.5 = -6.508925726 x = -6.508925726 Simplifying x = -6.508925726Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.508925726, -6.508925726}
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