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Simplifying 0 = -4.9x2 + 9x + 400 Reorder the terms: 0 = 400 + 9x + -4.9x2 Solving 0 = 400 + 9x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + -9x + 4.9x2 = 400 + 9x + -4.9x2 + -400 + -9x + 4.9x2 Reorder the terms: -400 + -9x + 4.9x2 = 400 + -400 + 9x + -9x + -4.9x2 + 4.9x2 Combine like terms: 400 + -400 = 0 -400 + -9x + 4.9x2 = 0 + 9x + -9x + -4.9x2 + 4.9x2 -400 + -9x + 4.9x2 = 9x + -9x + -4.9x2 + 4.9x2 Combine like terms: 9x + -9x = 0 -400 + -9x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -400 + -9x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -400 + -9x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -81.63265306 + -1.836734694x + x2 = 0 Move the constant term to the right: Add '81.63265306' to each side of the equation. -81.63265306 + -1.836734694x + 81.63265306 + x2 = 0 + 81.63265306 Reorder the terms: -81.63265306 + 81.63265306 + -1.836734694x + x2 = 0 + 81.63265306 Combine like terms: -81.63265306 + 81.63265306 = 0.00000000 0.00000000 + -1.836734694x + x2 = 0 + 81.63265306 -1.836734694x + x2 = 0 + 81.63265306 Combine like terms: 0 + 81.63265306 = 81.63265306 -1.836734694x + x2 = 81.63265306 The x term is -1.836734694x. Take half its coefficient (-0.918367347). Square it (0.8433985840) and add it to both sides. Add '0.8433985840' to each side of the equation. -1.836734694x + 0.8433985840 + x2 = 81.63265306 + 0.8433985840 Reorder the terms: 0.8433985840 + -1.836734694x + x2 = 81.63265306 + 0.8433985840 Combine like terms: 81.63265306 + 0.8433985840 = 82.476051644 0.8433985840 + -1.836734694x + x2 = 82.476051644 Factor a perfect square on the left side: (x + -0.918367347)(x + -0.918367347) = 82.476051644 Calculate the square root of the right side: 9.081632653 Break this problem into two subproblems by setting (x + -0.918367347) equal to 9.081632653 and -9.081632653.Subproblem 1
x + -0.918367347 = 9.081632653 Simplifying x + -0.918367347 = 9.081632653 Reorder the terms: -0.918367347 + x = 9.081632653 Solving -0.918367347 + x = 9.081632653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = 9.081632653 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = 9.081632653 + 0.918367347 x = 9.081632653 + 0.918367347 Combine like terms: 9.081632653 + 0.918367347 = 10 x = 10 Simplifying x = 10Subproblem 2
x + -0.918367347 = -9.081632653 Simplifying x + -0.918367347 = -9.081632653 Reorder the terms: -0.918367347 + x = -9.081632653 Solving -0.918367347 + x = -9.081632653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.918367347' to each side of the equation. -0.918367347 + 0.918367347 + x = -9.081632653 + 0.918367347 Combine like terms: -0.918367347 + 0.918367347 = 0.000000000 0.000000000 + x = -9.081632653 + 0.918367347 x = -9.081632653 + 0.918367347 Combine like terms: -9.081632653 + 0.918367347 = -8.163265306 x = -8.163265306 Simplifying x = -8.163265306Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -8.163265306}
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