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Simplifying 0 = x2 + -20x + -10 Reorder the terms: 0 = -10 + -20x + x2 Solving 0 = -10 + -20x + x2 Solving for variable 'x'. Combine like terms: 0 + 10 = 10 10 + 20x + -1x2 = -10 + -20x + x2 + 10 + 20x + -1x2 Reorder the terms: 10 + 20x + -1x2 = -10 + 10 + -20x + 20x + x2 + -1x2 Combine like terms: -10 + 10 = 0 10 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 10 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 10 + 20x + -1x2 = 0 + x2 + -1x2 10 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -20x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -20x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -20x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -20x + x2 = 0 + 10 -20x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -20x + x2 = 10 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 = 10 + 100 Reorder the terms: 100 + -20x + x2 = 10 + 100 Combine like terms: 10 + 100 = 110 100 + -20x + x2 = 110 Factor a perfect square on the left side: (x + -10)(x + -10) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (x + -10) equal to 10.488088482 and -10.488088482.Subproblem 1
x + -10 = 10.488088482 Simplifying x + -10 = 10.488088482 Reorder the terms: -10 + x = 10.488088482 Solving -10 + x = 10.488088482 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 = 10.488088482 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.488088482 + 10 x = 10.488088482 + 10 Combine like terms: 10.488088482 + 10 = 20.488088482 x = 20.488088482 Simplifying x = 20.488088482Subproblem 2
x + -10 = -10.488088482 Simplifying x + -10 = -10.488088482 Reorder the terms: -10 + x = -10.488088482 Solving -10 + x = -10.488088482 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 = -10.488088482 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.488088482 + 10 x = -10.488088482 + 10 Combine like terms: -10.488088482 + 10 = -0.488088482 x = -0.488088482 Simplifying x = -0.488088482Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.488088482, -0.488088482}
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