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Simplifying 9x2 + -2.25x + -139.5 = 0 Reorder the terms: -139.5 + -2.25x + 9x2 = 0 Solving -139.5 + -2.25x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -15.5 + -0.25x + x2 = 0 Move the constant term to the right: Add '15.5' to each side of the equation. -15.5 + -0.25x + 15.5 + x2 = 0 + 15.5 Reorder the terms: -15.5 + 15.5 + -0.25x + x2 = 0 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + -0.25x + x2 = 0 + 15.5 -0.25x + x2 = 0 + 15.5 Combine like terms: 0 + 15.5 = 15.5 -0.25x + x2 = 15.5 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 15.5 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 15.5 + 0.015625 Combine like terms: 15.5 + 0.015625 = 15.515625 0.015625 + -0.25x + x2 = 15.515625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 15.515625 Calculate the square root of the right side: 3.938987814 Break this problem into two subproblems by setting (x + -0.125) equal to 3.938987814 and -3.938987814.Subproblem 1
x + -0.125 = 3.938987814 Simplifying x + -0.125 = 3.938987814 Reorder the terms: -0.125 + x = 3.938987814 Solving -0.125 + x = 3.938987814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 3.938987814 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 3.938987814 + 0.125 x = 3.938987814 + 0.125 Combine like terms: 3.938987814 + 0.125 = 4.063987814 x = 4.063987814 Simplifying x = 4.063987814Subproblem 2
x + -0.125 = -3.938987814 Simplifying x + -0.125 = -3.938987814 Reorder the terms: -0.125 + x = -3.938987814 Solving -0.125 + x = -3.938987814 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -3.938987814 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -3.938987814 + 0.125 x = -3.938987814 + 0.125 Combine like terms: -3.938987814 + 0.125 = -3.813987814 x = -3.813987814 Simplifying x = -3.813987814Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.063987814, -3.813987814}
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