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Simplifying 15x2 + 1193.4 = 270x Reorder the terms: 1193.4 + 15x2 = 270x Solving 1193.4 + 15x2 = 270x Solving for variable 'x'. Reorder the terms: 1193.4 + -270x + 15x2 = 270x + -270x Combine like terms: 270x + -270x = 0 1193.4 + -270x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. 79.56 + -18x + x2 = 0 Move the constant term to the right: Add '-79.56' to each side of the equation. 79.56 + -18x + -79.56 + x2 = 0 + -79.56 Reorder the terms: 79.56 + -79.56 + -18x + x2 = 0 + -79.56 Combine like terms: 79.56 + -79.56 = 0.00 0.00 + -18x + x2 = 0 + -79.56 -18x + x2 = 0 + -79.56 Combine like terms: 0 + -79.56 = -79.56 -18x + x2 = -79.56 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -79.56 + 81 Reorder the terms: 81 + -18x + x2 = -79.56 + 81 Combine like terms: -79.56 + 81 = 1.44 81 + -18x + x2 = 1.44 Factor a perfect square on the left side: (x + -9)(x + -9) = 1.44 Calculate the square root of the right side: 1.2 Break this problem into two subproblems by setting (x + -9) equal to 1.2 and -1.2.Subproblem 1
x + -9 = 1.2 Simplifying x + -9 = 1.2 Reorder the terms: -9 + x = 1.2 Solving -9 + x = 1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 1.2 + 9 Combine like terms: -9 + 9 = 0 0 + x = 1.2 + 9 x = 1.2 + 9 Combine like terms: 1.2 + 9 = 10.2 x = 10.2 Simplifying x = 10.2Subproblem 2
x + -9 = -1.2 Simplifying x + -9 = -1.2 Reorder the terms: -9 + x = -1.2 Solving -9 + x = -1.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -1.2 + 9 Combine like terms: -9 + 9 = 0 0 + x = -1.2 + 9 x = -1.2 + 9 Combine like terms: -1.2 + 9 = 7.8 x = 7.8 Simplifying x = 7.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.2, 7.8}
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