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Simplifying 30x + (20 + -1x) * x = 100 Reorder the terms for easier multiplication: 30x + x(20 + -1x) = 100 30x + (20 * x + -1x * x) = 100 30x + (20x + -1x2) = 100 Combine like terms: 30x + 20x = 50x 50x + -1x2 = 100 Solving 50x + -1x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 50x + -1x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 50x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 100 + -50x + x2 = 0 Move the constant term to the right: Add '-100' to each side of the equation. 100 + -50x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -50x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -50x + x2 = 0 + -100 -50x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -50x + x2 = -100 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -100 + 625 Reorder the terms: 625 + -50x + x2 = -100 + 625 Combine like terms: -100 + 625 = 525 625 + -50x + x2 = 525 Factor a perfect square on the left side: (x + -25)(x + -25) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + -25) equal to 22.912878475 and -22.912878475.Subproblem 1
x + -25 = 22.912878475 Simplifying x + -25 = 22.912878475 Reorder the terms: -25 + x = 22.912878475 Solving -25 + x = 22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 22.912878475 + 25 Combine like terms: -25 + 25 = 0 0 + x = 22.912878475 + 25 x = 22.912878475 + 25 Combine like terms: 22.912878475 + 25 = 47.912878475 x = 47.912878475 Simplifying x = 47.912878475Subproblem 2
x + -25 = -22.912878475 Simplifying x + -25 = -22.912878475 Reorder the terms: -25 + x = -22.912878475 Solving -25 + x = -22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -22.912878475 + 25 Combine like terms: -25 + 25 = 0 0 + x = -22.912878475 + 25 x = -22.912878475 + 25 Combine like terms: -22.912878475 + 25 = 2.087121525 x = 2.087121525 Simplifying x = 2.087121525Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.912878475, 2.087121525}
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