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Simplifying x + 13 = (x + 12)(x + -25) Reorder the terms: 13 + x = (x + 12)(x + -25) Reorder the terms: 13 + x = (12 + x)(x + -25) Reorder the terms: 13 + x = (12 + x)(-25 + x) Multiply (12 + x) * (-25 + x) 13 + x = (12(-25 + x) + x(-25 + x)) 13 + x = ((-25 * 12 + x * 12) + x(-25 + x)) 13 + x = ((-300 + 12x) + x(-25 + x)) 13 + x = (-300 + 12x + (-25 * x + x * x)) 13 + x = (-300 + 12x + (-25x + x2)) Combine like terms: 12x + -25x = -13x 13 + x = (-300 + -13x + x2) Solving 13 + x = -300 + -13x + x2 Solving for variable 'x'. Reorder the terms: 13 + 300 + x + 13x + -1x2 = -300 + -13x + x2 + 300 + 13x + -1x2 Combine like terms: 13 + 300 = 313 313 + x + 13x + -1x2 = -300 + -13x + x2 + 300 + 13x + -1x2 Combine like terms: x + 13x = 14x 313 + 14x + -1x2 = -300 + -13x + x2 + 300 + 13x + -1x2 Reorder the terms: 313 + 14x + -1x2 = -300 + 300 + -13x + 13x + x2 + -1x2 Combine like terms: -300 + 300 = 0 313 + 14x + -1x2 = 0 + -13x + 13x + x2 + -1x2 313 + 14x + -1x2 = -13x + 13x + x2 + -1x2 Combine like terms: -13x + 13x = 0 313 + 14x + -1x2 = 0 + x2 + -1x2 313 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 313 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -313 + -14x + x2 = 0 Move the constant term to the right: Add '313' to each side of the equation. -313 + -14x + 313 + x2 = 0 + 313 Reorder the terms: -313 + 313 + -14x + x2 = 0 + 313 Combine like terms: -313 + 313 = 0 0 + -14x + x2 = 0 + 313 -14x + x2 = 0 + 313 Combine like terms: 0 + 313 = 313 -14x + x2 = 313 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 = 313 + 49 Reorder the terms: 49 + -14x + x2 = 313 + 49 Combine like terms: 313 + 49 = 362 49 + -14x + x2 = 362 Factor a perfect square on the left side: (x + -7)(x + -7) = 362 Calculate the square root of the right side: 19.02629759 Break this problem into two subproblems by setting (x + -7) equal to 19.02629759 and -19.02629759.Subproblem 1
x + -7 = 19.02629759 Simplifying x + -7 = 19.02629759 Reorder the terms: -7 + x = 19.02629759 Solving -7 + x = 19.02629759 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 = 19.02629759 + 7 Combine like terms: -7 + 7 = 0 0 + x = 19.02629759 + 7 x = 19.02629759 + 7 Combine like terms: 19.02629759 + 7 = 26.02629759 x = 26.02629759 Simplifying x = 26.02629759Subproblem 2
x + -7 = -19.02629759 Simplifying x + -7 = -19.02629759 Reorder the terms: -7 + x = -19.02629759 Solving -7 + x = -19.02629759 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 = -19.02629759 + 7 Combine like terms: -7 + 7 = 0 0 + x = -19.02629759 + 7 x = -19.02629759 + 7 Combine like terms: -19.02629759 + 7 = -12.02629759 x = -12.02629759 Simplifying x = -12.02629759Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.02629759, -12.02629759}
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