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Simplifying 1530 = (x + 15)(x + -10) Reorder the terms: 1530 = (15 + x)(x + -10) Reorder the terms: 1530 = (15 + x)(-10 + x) Multiply (15 + x) * (-10 + x) 1530 = (15(-10 + x) + x(-10 + x)) 1530 = ((-10 * 15 + x * 15) + x(-10 + x)) 1530 = ((-150 + 15x) + x(-10 + x)) 1530 = (-150 + 15x + (-10 * x + x * x)) 1530 = (-150 + 15x + (-10x + x2)) Combine like terms: 15x + -10x = 5x 1530 = (-150 + 5x + x2) Solving 1530 = -150 + 5x + x2 Solving for variable 'x'. Combine like terms: 1530 + 150 = 1680 1680 + -5x + -1x2 = -150 + 5x + x2 + 150 + -5x + -1x2 Reorder the terms: 1680 + -5x + -1x2 = -150 + 150 + 5x + -5x + x2 + -1x2 Combine like terms: -150 + 150 = 0 1680 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 1680 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 1680 + -5x + -1x2 = 0 + x2 + -1x2 1680 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1680 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1680 + 5x + x2 = 0 Move the constant term to the right: Add '1680' to each side of the equation. -1680 + 5x + 1680 + x2 = 0 + 1680 Reorder the terms: -1680 + 1680 + 5x + x2 = 0 + 1680 Combine like terms: -1680 + 1680 = 0 0 + 5x + x2 = 0 + 1680 5x + x2 = 0 + 1680 Combine like terms: 0 + 1680 = 1680 5x + x2 = 1680 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 1680 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 1680 + 6.25 Combine like terms: 1680 + 6.25 = 1686.25 6.25 + 5x + x2 = 1686.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 1686.25 Calculate the square root of the right side: 41.063974479 Break this problem into two subproblems by setting (x + 2.5) equal to 41.063974479 and -41.063974479.Subproblem 1
x + 2.5 = 41.063974479 Simplifying x + 2.5 = 41.063974479 Reorder the terms: 2.5 + x = 41.063974479 Solving 2.5 + x = 41.063974479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 41.063974479 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 41.063974479 + -2.5 x = 41.063974479 + -2.5 Combine like terms: 41.063974479 + -2.5 = 38.563974479 x = 38.563974479 Simplifying x = 38.563974479Subproblem 2
x + 2.5 = -41.063974479 Simplifying x + 2.5 = -41.063974479 Reorder the terms: 2.5 + x = -41.063974479 Solving 2.5 + x = -41.063974479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -41.063974479 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -41.063974479 + -2.5 x = -41.063974479 + -2.5 Combine like terms: -41.063974479 + -2.5 = -43.563974479 x = -43.563974479 Simplifying x = -43.563974479Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.563974479, -43.563974479}
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