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Simplifying 15x2 = 9.75 + 6.25x + x2 Solving 15x2 = 9.75 + 6.25x + x2 Solving for variable 'x'. Reorder the terms: -9.75 + -6.25x + 15x2 + -1x2 = 9.75 + 6.25x + x2 + -9.75 + -6.25x + -1x2 Combine like terms: 15x2 + -1x2 = 14x2 -9.75 + -6.25x + 14x2 = 9.75 + 6.25x + x2 + -9.75 + -6.25x + -1x2 Reorder the terms: -9.75 + -6.25x + 14x2 = 9.75 + -9.75 + 6.25x + -6.25x + x2 + -1x2 Combine like terms: 9.75 + -9.75 = 0.00 -9.75 + -6.25x + 14x2 = 0.00 + 6.25x + -6.25x + x2 + -1x2 -9.75 + -6.25x + 14x2 = 6.25x + -6.25x + x2 + -1x2 Combine like terms: 6.25x + -6.25x = 0.00 -9.75 + -6.25x + 14x2 = 0.00 + x2 + -1x2 -9.75 + -6.25x + 14x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9.75 + -6.25x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.6964285714 + -0.4464285714x + x2 = 0 Move the constant term to the right: Add '0.6964285714' to each side of the equation. -0.6964285714 + -0.4464285714x + 0.6964285714 + x2 = 0 + 0.6964285714 Reorder the terms: -0.6964285714 + 0.6964285714 + -0.4464285714x + x2 = 0 + 0.6964285714 Combine like terms: -0.6964285714 + 0.6964285714 = 0.0000000000 0.0000000000 + -0.4464285714x + x2 = 0 + 0.6964285714 -0.4464285714x + x2 = 0 + 0.6964285714 Combine like terms: 0 + 0.6964285714 = 0.6964285714 -0.4464285714x + x2 = 0.6964285714 The x term is -0.4464285714x. Take half its coefficient (-0.2232142857). Square it (0.04982461734) and add it to both sides. Add '0.04982461734' to each side of the equation. -0.4464285714x + 0.04982461734 + x2 = 0.6964285714 + 0.04982461734 Reorder the terms: 0.04982461734 + -0.4464285714x + x2 = 0.6964285714 + 0.04982461734 Combine like terms: 0.6964285714 + 0.04982461734 = 0.74625318874 0.04982461734 + -0.4464285714x + x2 = 0.74625318874 Factor a perfect square on the left side: (x + -0.2232142857)(x + -0.2232142857) = 0.74625318874 Calculate the square root of the right side: 0.863859473 Break this problem into two subproblems by setting (x + -0.2232142857) equal to 0.863859473 and -0.863859473.Subproblem 1
x + -0.2232142857 = 0.863859473 Simplifying x + -0.2232142857 = 0.863859473 Reorder the terms: -0.2232142857 + x = 0.863859473 Solving -0.2232142857 + x = 0.863859473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2232142857' to each side of the equation. -0.2232142857 + 0.2232142857 + x = 0.863859473 + 0.2232142857 Combine like terms: -0.2232142857 + 0.2232142857 = 0.0000000000 0.0000000000 + x = 0.863859473 + 0.2232142857 x = 0.863859473 + 0.2232142857 Combine like terms: 0.863859473 + 0.2232142857 = 1.0870737587 x = 1.0870737587 Simplifying x = 1.0870737587Subproblem 2
x + -0.2232142857 = -0.863859473 Simplifying x + -0.2232142857 = -0.863859473 Reorder the terms: -0.2232142857 + x = -0.863859473 Solving -0.2232142857 + x = -0.863859473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2232142857' to each side of the equation. -0.2232142857 + 0.2232142857 + x = -0.863859473 + 0.2232142857 Combine like terms: -0.2232142857 + 0.2232142857 = 0.0000000000 0.0000000000 + x = -0.863859473 + 0.2232142857 x = -0.863859473 + 0.2232142857 Combine like terms: -0.863859473 + 0.2232142857 = -0.6406451873 x = -0.6406451873 Simplifying x = -0.6406451873Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0870737587, -0.6406451873}
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