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Simplifying 15x2 + -304x = 540 Reorder the terms: -304x + 15x2 = 540 Solving -304x + 15x2 = 540 Solving for variable 'x'. Reorder the terms: -540 + -304x + 15x2 = 540 + -540 Combine like terms: 540 + -540 = 0 -540 + -304x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -36 + -20.26666667x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -20.26666667x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -20.26666667x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -20.26666667x + x2 = 0 + 36 -20.26666667x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -20.26666667x + x2 = 36 The x term is -20.26666667x. Take half its coefficient (-10.13333334). Square it (102.6844446) and add it to both sides. Add '102.6844446' to each side of the equation. -20.26666667x + 102.6844446 + x2 = 36 + 102.6844446 Reorder the terms: 102.6844446 + -20.26666667x + x2 = 36 + 102.6844446 Combine like terms: 36 + 102.6844446 = 138.6844446 102.6844446 + -20.26666667x + x2 = 138.6844446 Factor a perfect square on the left side: (x + -10.13333334)(x + -10.13333334) = 138.6844446 Calculate the square root of the right side: 11.776435989 Break this problem into two subproblems by setting (x + -10.13333334) equal to 11.776435989 and -11.776435989.Subproblem 1
x + -10.13333334 = 11.776435989 Simplifying x + -10.13333334 = 11.776435989 Reorder the terms: -10.13333334 + x = 11.776435989 Solving -10.13333334 + x = 11.776435989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.13333334' to each side of the equation. -10.13333334 + 10.13333334 + x = 11.776435989 + 10.13333334 Combine like terms: -10.13333334 + 10.13333334 = 0.00000000 0.00000000 + x = 11.776435989 + 10.13333334 x = 11.776435989 + 10.13333334 Combine like terms: 11.776435989 + 10.13333334 = 21.909769329 x = 21.909769329 Simplifying x = 21.909769329Subproblem 2
x + -10.13333334 = -11.776435989 Simplifying x + -10.13333334 = -11.776435989 Reorder the terms: -10.13333334 + x = -11.776435989 Solving -10.13333334 + x = -11.776435989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.13333334' to each side of the equation. -10.13333334 + 10.13333334 + x = -11.776435989 + 10.13333334 Combine like terms: -10.13333334 + 10.13333334 = 0.00000000 0.00000000 + x = -11.776435989 + 10.13333334 x = -11.776435989 + 10.13333334 Combine like terms: -11.776435989 + 10.13333334 = -1.643102649 x = -1.643102649 Simplifying x = -1.643102649Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.909769329, -1.643102649}
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