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Simplifying 0.1(x2 + 9x + -360) = 0 Reorder the terms: 0.1(-360 + 9x + x2) = 0 (-360 * 0.1 + 9x * 0.1 + x2 * 0.1) = 0 (-36 + 0.9x + 0.1x2) = 0 Solving -36 + 0.9x + 0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -360 + 9x + x2 = 0 Move the constant term to the right: Add '360' to each side of the equation. -360 + 9x + 360 + x2 = 0 + 360 Reorder the terms: -360 + 360 + 9x + x2 = 0 + 360 Combine like terms: -360 + 360 = 0 0 + 9x + x2 = 0 + 360 9x + x2 = 0 + 360 Combine like terms: 0 + 360 = 360 9x + x2 = 360 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 360 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 360 + 20.25 Combine like terms: 360 + 20.25 = 380.25 20.25 + 9x + x2 = 380.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 380.25 Calculate the square root of the right side: 19.5 Break this problem into two subproblems by setting (x + 4.5) equal to 19.5 and -19.5.Subproblem 1
x + 4.5 = 19.5 Simplifying x + 4.5 = 19.5 Reorder the terms: 4.5 + x = 19.5 Solving 4.5 + x = 19.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 19.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 19.5 + -4.5 x = 19.5 + -4.5 Combine like terms: 19.5 + -4.5 = 15 x = 15 Simplifying x = 15Subproblem 2
x + 4.5 = -19.5 Simplifying x + 4.5 = -19.5 Reorder the terms: 4.5 + x = -19.5 Solving 4.5 + x = -19.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -19.5 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -19.5 + -4.5 x = -19.5 + -4.5 Combine like terms: -19.5 + -4.5 = -24 x = -24 Simplifying x = -24Solution
The solution to the problem is based on the solutions from the subproblems. x = {15, -24}
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