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Simplifying 9970 = x2 + -20x + 7 Reorder the terms: 9970 = 7 + -20x + x2 Solving 9970 = 7 + -20x + x2 Solving for variable 'x'. Combine like terms: 9970 + -7 = 9963 9963 + 20x + -1x2 = 7 + -20x + x2 + -7 + 20x + -1x2 Reorder the terms: 9963 + 20x + -1x2 = 7 + -7 + -20x + 20x + x2 + -1x2 Combine like terms: 7 + -7 = 0 9963 + 20x + -1x2 = 0 + -20x + 20x + x2 + -1x2 9963 + 20x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 9963 + 20x + -1x2 = 0 + x2 + -1x2 9963 + 20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 9963 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9963 + -20x + x2 = 0 Move the constant term to the right: Add '9963' to each side of the equation. -9963 + -20x + 9963 + x2 = 0 + 9963 Reorder the terms: -9963 + 9963 + -20x + x2 = 0 + 9963 Combine like terms: -9963 + 9963 = 0 0 + -20x + x2 = 0 + 9963 -20x + x2 = 0 + 9963 Combine like terms: 0 + 9963 = 9963 -20x + x2 = 9963 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 = 9963 + 100 Reorder the terms: 100 + -20x + x2 = 9963 + 100 Combine like terms: 9963 + 100 = 10063 100 + -20x + x2 = 10063 Factor a perfect square on the left side: (x + -10)(x + -10) = 10063 Calculate the square root of the right side: 100.314505432 Break this problem into two subproblems by setting (x + -10) equal to 100.314505432 and -100.314505432.Subproblem 1
x + -10 = 100.314505432 Simplifying x + -10 = 100.314505432 Reorder the terms: -10 + x = 100.314505432 Solving -10 + x = 100.314505432 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 = 100.314505432 + 10 Combine like terms: -10 + 10 = 0 0 + x = 100.314505432 + 10 x = 100.314505432 + 10 Combine like terms: 100.314505432 + 10 = 110.314505432 x = 110.314505432 Simplifying x = 110.314505432Subproblem 2
x + -10 = -100.314505432 Simplifying x + -10 = -100.314505432 Reorder the terms: -10 + x = -100.314505432 Solving -10 + x = -100.314505432 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 = -100.314505432 + 10 Combine like terms: -10 + 10 = 0 0 + x = -100.314505432 + 10 x = -100.314505432 + 10 Combine like terms: -100.314505432 + 10 = -90.314505432 x = -90.314505432 Simplifying x = -90.314505432Solution
The solution to the problem is based on the solutions from the subproblems. x = {110.314505432, -90.314505432}
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