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Simplifying 20 = 0.04x2 + -0.09x + 1.2 Reorder the terms: 20 = 1.2 + -0.09x + 0.04x2 Solving 20 = 1.2 + -0.09x + 0.04x2 Solving for variable 'x'. Combine like terms: 20 + -1.2 = 18.8 18.8 + 0.09x + -0.04x2 = 1.2 + -0.09x + 0.04x2 + -1.2 + 0.09x + -0.04x2 Reorder the terms: 18.8 + 0.09x + -0.04x2 = 1.2 + -1.2 + -0.09x + 0.09x + 0.04x2 + -0.04x2 Combine like terms: 1.2 + -1.2 = 0.0 18.8 + 0.09x + -0.04x2 = 0.0 + -0.09x + 0.09x + 0.04x2 + -0.04x2 18.8 + 0.09x + -0.04x2 = -0.09x + 0.09x + 0.04x2 + -0.04x2 Combine like terms: -0.09x + 0.09x = 0.00 18.8 + 0.09x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2 18.8 + 0.09x + -0.04x2 = 0.04x2 + -0.04x2 Combine like terms: 0.04x2 + -0.04x2 = 0.00 18.8 + 0.09x + -0.04x2 = 0.00 Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -470 + -2.25x + x2 = 0 Move the constant term to the right: Add '470' to each side of the equation. -470 + -2.25x + 470 + x2 = 0 + 470 Reorder the terms: -470 + 470 + -2.25x + x2 = 0 + 470 Combine like terms: -470 + 470 = 0 0 + -2.25x + x2 = 0 + 470 -2.25x + x2 = 0 + 470 Combine like terms: 0 + 470 = 470 -2.25x + x2 = 470 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 470 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 470 + 1.265625 Combine like terms: 470 + 1.265625 = 471.265625 1.265625 + -2.25x + x2 = 471.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 471.265625 Calculate the square root of the right side: 21.708653229 Break this problem into two subproblems by setting (x + -1.125) equal to 21.708653229 and -21.708653229.Subproblem 1
x + -1.125 = 21.708653229 Simplifying x + -1.125 = 21.708653229 Reorder the terms: -1.125 + x = 21.708653229 Solving -1.125 + x = 21.708653229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 21.708653229 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 21.708653229 + 1.125 x = 21.708653229 + 1.125 Combine like terms: 21.708653229 + 1.125 = 22.833653229 x = 22.833653229 Simplifying x = 22.833653229Subproblem 2
x + -1.125 = -21.708653229 Simplifying x + -1.125 = -21.708653229 Reorder the terms: -1.125 + x = -21.708653229 Solving -1.125 + x = -21.708653229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -21.708653229 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -21.708653229 + 1.125 x = -21.708653229 + 1.125 Combine like terms: -21.708653229 + 1.125 = -20.583653229 x = -20.583653229 Simplifying x = -20.583653229Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.833653229, -20.583653229}
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