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Simplifying 1440 = x(x + -19) Reorder the terms: 1440 = x(-19 + x) 1440 = (-19 * x + x * x) 1440 = (-19x + x2) Solving 1440 = -19x + x2 Solving for variable 'x'. Reorder the terms: 1440 + 19x + -1x2 = -19x + 19x + x2 + -1x2 Combine like terms: -19x + 19x = 0 1440 + 19x + -1x2 = 0 + x2 + -1x2 1440 + 19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1440 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1440 + -19x + x2 = 0 Move the constant term to the right: Add '1440' to each side of the equation. -1440 + -19x + 1440 + x2 = 0 + 1440 Reorder the terms: -1440 + 1440 + -19x + x2 = 0 + 1440 Combine like terms: -1440 + 1440 = 0 0 + -19x + x2 = 0 + 1440 -19x + x2 = 0 + 1440 Combine like terms: 0 + 1440 = 1440 -19x + x2 = 1440 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 1440 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 1440 + 90.25 Combine like terms: 1440 + 90.25 = 1530.25 90.25 + -19x + x2 = 1530.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 1530.25 Calculate the square root of the right side: 39.118409988 Break this problem into two subproblems by setting (x + -9.5) equal to 39.118409988 and -39.118409988.Subproblem 1
x + -9.5 = 39.118409988 Simplifying x + -9.5 = 39.118409988 Reorder the terms: -9.5 + x = 39.118409988 Solving -9.5 + x = 39.118409988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 39.118409988 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 39.118409988 + 9.5 x = 39.118409988 + 9.5 Combine like terms: 39.118409988 + 9.5 = 48.618409988 x = 48.618409988 Simplifying x = 48.618409988Subproblem 2
x + -9.5 = -39.118409988 Simplifying x + -9.5 = -39.118409988 Reorder the terms: -9.5 + x = -39.118409988 Solving -9.5 + x = -39.118409988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -39.118409988 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -39.118409988 + 9.5 x = -39.118409988 + 9.5 Combine like terms: -39.118409988 + 9.5 = -29.618409988 x = -29.618409988 Simplifying x = -29.618409988Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.618409988, -29.618409988}
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