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Simplifying 20x + 70 = x2 + 30 Reorder the terms: 70 + 20x = x2 + 30 Reorder the terms: 70 + 20x = 30 + x2 Solving 70 + 20x = 30 + x2 Solving for variable 'x'. Reorder the terms: 70 + -30 + 20x + -1x2 = 30 + x2 + -30 + -1x2 Combine like terms: 70 + -30 = 40 40 + 20x + -1x2 = 30 + x2 + -30 + -1x2 Reorder the terms: 40 + 20x + -1x2 = 30 + -30 + x2 + -1x2 Combine like terms: 30 + -30 = 0 40 + 20x + -1x2 = 0 + x2 + -1x2 40 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -20x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -20x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -20x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -20x + x2 = 0 + 40 -20x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -20x + x2 = 40 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 40 + 100 Reorder the terms: 100 + -20x + x2 = 40 + 100 Combine like terms: 40 + 100 = 140 100 + -20x + x2 = 140 Factor a perfect square on the left side: (x + -10)(x + -10) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + -10) equal to 11.832159566 and -11.832159566.Subproblem 1
x + -10 = 11.832159566 Simplifying x + -10 = 11.832159566 Reorder the terms: -10 + x = 11.832159566 Solving -10 + x = 11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 11.832159566 + 10 Combine like terms: -10 + 10 = 0 0 + x = 11.832159566 + 10 x = 11.832159566 + 10 Combine like terms: 11.832159566 + 10 = 21.832159566 x = 21.832159566 Simplifying x = 21.832159566Subproblem 2
x + -10 = -11.832159566 Simplifying x + -10 = -11.832159566 Reorder the terms: -10 + x = -11.832159566 Solving -10 + x = -11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -11.832159566 + 10 Combine like terms: -10 + 10 = 0 0 + x = -11.832159566 + 10 x = -11.832159566 + 10 Combine like terms: -11.832159566 + 10 = -1.832159566 x = -1.832159566 Simplifying x = -1.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.832159566, -1.832159566}
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