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Simplifying x = x2 + -20x + -70 Reorder the terms: x = -70 + -20x + x2 Solving x = -70 + -20x + x2 Solving for variable 'x'. Reorder the terms: 70 + x + 20x + -1x2 = -70 + -20x + x2 + 70 + 20x + -1x2 Combine like terms: x + 20x = 21x 70 + 21x + -1x2 = -70 + -20x + x2 + 70 + 20x + -1x2 Reorder the terms: 70 + 21x + -1x2 = -70 + 70 + -20x + 20x + x2 + -1x2 Combine like terms: -70 + 70 = 0 70 + 21x + -1x2 = 0 + -20x + 20x + x2 + -1x2 70 + 21x + -1x2 = -20x + 20x + x2 + -1x2 Combine like terms: -20x + 20x = 0 70 + 21x + -1x2 = 0 + x2 + -1x2 70 + 21x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 70 + 21x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -70 + -21x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -21x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -21x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -21x + x2 = 0 + 70 -21x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -21x + x2 = 70 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 70 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 70 + 110.25 Combine like terms: 70 + 110.25 = 180.25 110.25 + -21x + x2 = 180.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 180.25 Calculate the square root of the right side: 13.425721582 Break this problem into two subproblems by setting (x + -10.5) equal to 13.425721582 and -13.425721582.Subproblem 1
x + -10.5 = 13.425721582 Simplifying x + -10.5 = 13.425721582 Reorder the terms: -10.5 + x = 13.425721582 Solving -10.5 + x = 13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 13.425721582 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 13.425721582 + 10.5 x = 13.425721582 + 10.5 Combine like terms: 13.425721582 + 10.5 = 23.925721582 x = 23.925721582 Simplifying x = 23.925721582Subproblem 2
x + -10.5 = -13.425721582 Simplifying x + -10.5 = -13.425721582 Reorder the terms: -10.5 + x = -13.425721582 Solving -10.5 + x = -13.425721582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -13.425721582 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -13.425721582 + 10.5 x = -13.425721582 + 10.5 Combine like terms: -13.425721582 + 10.5 = -2.925721582 x = -2.925721582 Simplifying x = -2.925721582Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.925721582, -2.925721582}
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